West Ham temporarily moved up to fifth in the Premier League after overcoming relegation-threatened Everton 2-1 at the London Stadium on Super Sunday.
Jarrod Bowen struck on his return to the side after a four-game absence with a foot injury (58) to ensure the Hammers remain firmly in the hunt for Champions League qualification.
Aaron Cresswell had given the home side the lead with a brilliant free-kick (32) before Mason Holgate - who was a late selection after Donny van de Beek suffered an injury in the warm-up - equalised for Everton eight minutes after half time.
Bowen's response was immediate, and the visitors were reduced to 10 men when Michael Keane was sent off for a second bookable offence (65) in bringing down Michail Antonio - a third red card in Everton's last three games.
The result means Frank Lampard's side remain perilously close to the relegation zone - three points above 18th-placed Watford with two games in hand but only four points above Burnley, with the two sides facing each other next on Wednesday, live on Sky Sports.
West Ham slipped back to sixth position later on Sunday after Tottenham came from behind to thrash Newcastle 5-1 courtesy of four goals in a devastating 20-minute spell.
- Lampard confident of Everton survival | Moyes: They have quality to stay up
- How the teams lined up | Match stats
- Premier League table | Fixtures | Results
Concentration and discipline desert Everton
Lampard called for his Everton players to develop better resilience to improve the worst away record in England's top four divisions - just six points from a possible 42 on the road.
In fact, dropping all the way down to National League North and South, only one side - National League Dover - have performed worse away from home. Lampard blamed a poor reaction to adversity for such an appalling statistic, and they were up against it again as West Ham started the brighter of the two sides.
Pablo Fornals, on his return to the West Ham side, scuffed a presentable opportunity that was blocked by Keane from Ryan Fredericks' low cross after five minutes.
Keane was in the right place again to thwart a rasping drive from Antonio but Everton were indebted to Jordan Pickford to smother at the feet of Fornals moments later after the Spaniard was picked out by Said Benrahma.
Lampard was boosted by the return to the starting line-up of Dominic Calvert-Lewin - and Everton carved open their first decent chance on 29 minutes. Demarai Gray combined with Alex Iwobi in midfield to feed Richarlison but after the Brazilian had nipped around Lukasz Fabianski, Fredericks produced a vital recovery challenge.
It would prove a turning point as moments later, West Ham were in front. Bowen was upended by Holgate and from 25 yards out, Cresswell's delicious free-kick curled beyond the despairing Pickford.
It was another set-piece goal scored by West Ham and conceded by Everton, made all the more painful by it being scored by a boyhood Liverpool supporter as Cresswell celebrated in front of the travelling fans.
Richarlison continued to carry Everton's biggest threat and he ought to have levelled when he pounced on a mistake by Fredericks to latch onto Pickford's long ball with five minutes of the half remaining, but his effort with the outside of his right boot flashed over the bar.
West Ham deservedly led at the break and might have been further ahead on the stroke of the interval when Benrahma played through Antonio, who rounded Pickford but could only steer his shot into the side-netting from an acute angle.
Everton emerged re-energised for the restart and might have equalised when Declan Rice was dispossessed and Iwobi fed Calvert-Lewin but the striker clipped the crossbar at Fabianski's near post.
David Moyes wore a concerned look, and his grimace was even wider when Holgate's half volley found the bottom corner via a deflection off Fornals as West Ham failed to clear a corner.
Lampard sensed a turnaround but a lapse in concentration by Iwobi allowed West Ham to restore their advantage five minutes later. The Nigerian failed to collect Keane's pass and after Fornals had immediately played Antonio through on goal, Pickford could only divert his shot straight to Bowen for a simple finish.
Seven minutes later, things got even tougher for Lampard as Keane - already on a booking for a foul in the first half on Antonio - lunged in on the same player leaving referee Michael Oliver with no option but to dismiss Everton's captain.
Cresswell bent the ensuing free-kick just wide and Ben Godfrey would later deny Antonio the goal his performance deserved with a superb last-ditch tackle. Lampard was then left looking to the skies as Godfrey headed over in stoppage time.
West Ham weren't at their best, but they often haven't been in collecting points in the second half of this season - especially at home.
Their battle for fourth goes on under Moyes, a manager who once achieved such a glorious feat at Everton in 2005. How long ago that now feels for the blue half of Merseyside.
Moyes: This is just the starter
West Ham boss David Moyes: "We give him [Aaron Cresswell] a lot of stick because he practises free-kicks so much and has not had many goals. He has had a lot of assists in other ways. It was a real good free-kick today.
"It was a really good win and I thought the players did a really good job. I would like the standards and levels to be better. Coming back from international duty and getting the players back on it is never easy. It was a tough game. We huffed and puffed at times. We had opportunities but so did they.
"We have a huge game coming up on Thursday night. I would like to say that wasn't playing in my mind, but it clearly was. I'd like to say all the players have come through OK, Jarrod Bowen included.
"We know that Jarrod has goals in him. It was unfortunate the injury he got as we could have found him being part of the England squad. Gareth may look at him again in the summer if he keeps his form up. But for us he does a great job. Hopefully he is rejuvenated after the break and can play even better.
"This is just the starter. We have the main course coming up on Thursday and hopefully we can be quicker and sharper."
Lampard: I can't fault the players
Everton boss Frank Lampard: We're disappointed because we deserved at least a point from the game. At 1-1 I fancied us to score a second. There's a mistake and they break away and score. It drops to them. The first goal is a free-kick in the top corner.
"The reality is that we are in that kind of moment where everything is going against us - decisions, moments in games, red cards. I can't fault the players, their character, play generally. The performance was really positive and we have 10 games to perform like that again and more.
"We weren't so good at Palace but passion and desire has been there. Not many teams do it every week. The reason we are in this position is that we want to get better. Today it was there and this is a tough place to come. They are organised and have quality.
"But two or three seasons ago they were fighting relegation. Now look at them and where they are. That is the reality of football. The curve moves quickly and you need to make that work in your favour. It is not going our way at the moment, but we have to keep working. It is not easy to take positives from no points but we have to take positives from the performance.
"The red card changes plans. It is the third game in a row. Two of those sending-offs are yellows you can be frustrated with. One is not a sending-off. Allan against Newcastle should be overturned but people want to save face. It is difficult with 10 men. We kept going and the spirit and resilience in the team was really good."
Bowen delivers perfect response
West Ham forward Bowen, whose injury ruled him out of England's March international friendlies, says he couldn't have asked for much more on his return to the side.
Bowen has been involved in 17 Premier League goals this season for West Ham, with only Mohamed Salah (30) and Son Heung-Min (18) involved in more across the Premier League.
"That's what you want when you have been out," he told Sky Sports. "It has been four weeks, the time has been annoying but to come back into the starting XI and get the three points, don't think you can ask for much more.
"I tried to be as sharp as I could out there, I'm not going to be same as I was before injury just yet.
"We knew they would come out chasing the game, it was just about dealing with it. They got the goal and it was a kick in the teeth. It is about the reaction and we showed the reaction.
"We want to be as far into the competitions we can and keep winning. The great thing is winning games of football and we want to do that each game.
"I've said from the start of the season we will need the fans when there are highs and lows in football and they were brilliant again today."
Analysis: Everton must stick together in troubling times
Sky Sports' Ben Grounds at the London Stadium:
The misery continues for Everton. Bowen inflicted more away-day pain for Lampard's side but here they were the authors of their own downfall, beaten by their own lapse in concentration before the red mist descended.
Keane captained the side in the absence of Seamus Coleman but it was his tired challenge on Antonio which made life more difficult moments after West Ham had regained the lead.
Lampard had questioned his players' bottle - or words to that effect - after they capitulated at Crystal Palace in the FA Cup last time out, and they conceded poorly again just five minutes after equalising when Bowen struck.
Keane's second yellow card capped another miserable road trip for Lampard, and he simply cannot afford yet another fruitless jaunt away from Goodison Park on Wednesday in that crucial game against Burnley at Turf Moor.
Everton remain safe, for now, but defeat to Sean Dyche's side would close the gap to the bottom three to just a point. As Richarlison trudged disconsolately down the tunnel, Lampard must pull his troops together for the battle that lies ahead.
Former Everton winger David Ginola told Sky Sports:
"It gets worse and worse and when you are in a situation like that, especially when you have to play against teams who are competing against you and fighting relegation.
"The game against Burnley will be another crucial one for Frank Lampard. So many games lost already for a manager who all the fans were expecting to take the club out of that situation. They are under pressure and he is under pressure.
"You can lose one game but over a 38-game season, if you are in this position it's because you are not good enough."
Sky Sports' Graeme Souness:
"You can't fault that group for their effort but I'm afraid it just comes down to they have don't have enough quality at this level to be winning games away from home. They don't have enough quality and for me that's the top and bottom of it. The league doesn't lie."
West Ham boss David Moyes:
"I think Everton will be OK - when you've got the forward players they've got it gives you a great chance and they've got good players in wide areas. They should feel more positive about it but I've been there recently with West Ham and before with Sunderland when we didn't stay up. I feel they've got the quality that other clubs don't have but you just never know."
Lampard's unwanted record - Opta stats
- West Ham United have completed their first league double over Everton since the 1972-73 season, while this was only their second win in their last 14 home Premier League meetings with the Toffees (D4 L8).
- Since the start of October, Everton have won the fewest points in the Premier League (12) and are the only side in the division to not win an away game in that timeframe (P11 D2 L9).
- West Ham United have won 15 Premier League matches this season - after winning 19 last season, it's the first time they've won 15+ games in back-to-back seasons in the competition since doing so in three in a row between 1997-98 and 1999-00, with Everton manager Frank Lampard making the most appearances for the Hammers across those seasons (103).
- Frank Lampard has become the first Everton manager in Premier League history to lose his first four away matches in charge of the club in the competition, and the first at a single club since Paul Heckingbottom with Sheffield United last season.
What's next?
West Ham host Lyon in the first leg of their Europa League quarter-final on Thursday, April 7; kick-off 8pm.
Everton travel to Burnley in the Premier League on Wednesday, April 6 live on Sky Sports; kick-off 7.30pm.