Two glaring errors from Newcastle's Kieran Trippier allowed Dwight McNeil and Abdoulaye Doucoure to strike late on for Everton in a 3-0 win which lifts them out of the Premier League relegation zone.
Less than three weeks after being handed a 10-point deduction for financial issues which sent them into the bottom three, Everton are up to 17th and a point above third-bottom Luton.
McNeil was the match-winner at Nottingham Forest on Saturday and he pounced on Trippier's first mis-control before racing towards goal and finishing impressively past stand-in Newcastle stopper Martin Dubravka with 11 minutes left on the clock.
Jack Harrison then forced a similar mistake from the usually reliable Trippier before crossing for Doucoure to convert from close range and spark jubilant scenes among the home fans, who had again protested against the punishment handed down to their club, which has been appealed.
There was more joy to come, with Beto beating the offside trap deep into injury-time to score his first Premier League goal.
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Those mistakes from Trippier and Beto's long-awaited arrival on the scoresheet transformed the narrative of the night, which until that point had seen Everton again waste a series of chances at Goodison Park. Indeed, Dominic Calvert-Lewin's first-half unmarked volley from four yards out was a miss-of-the-season contender.
The returning Anthony Gordon threatened to punish his former club but could not silence the boos with an accurate finish despite three attempts, including a big opening when he caught James Tarkowski in possession in the Everton box.
But this was a tired performance from injury-hit Newcastle, who have fielded the same outfield players for four games in a row now. Eddie Howe's side have run out of steam. They stay seventh.
Injury-hit Newcastle showing the strain
As well as goalkeeper Nick Pope, Newcastle are missing 10 outfielders: Jacob Murphy, Dan Burn, Callum Wilson, Elliot Anderson, Sean Longstaff, Sven Botman, Joe Willock, Harvey Barnes, Javier Manquillo and Matt Targett. Jamaal Lascelles also appeared to go off injured on Thursday, while Sandro Tonali is suspended.
They were out-run by Everton 110km to 107km, with their opponents logging 151 sprints to Newcastle's 99. Howe said the lack of attacking options at their disposal is a 'big miss'.
"There are reasons behind every performance and we have struggled to change our players in-running," said Howe, when asked about the lack of alterations. "To have the attacking options we feel we need to change the game, that's not there for us and that's a big miss. There are some quality players, outstanding players that aren't with us at the moment.
"You can potentially do it for a short period of time, the longer you do it the harder it gets. That's not to say it's impossible. That's why I'm disappointed - I think it's a missed opportunity for us and we didn't really grab it and paid the price."
How Trippier helped Everton to victory...
Everton's finishing at Goodison Park has been poor all season and the team with the worst conversion rate in the Premier League going into this round of games kept up that trend for 79 minutes on Thursday, with Calvert-Lewin seeing two chances saved by Dubravka before his shocking close-range volley was skied over.
McNeil also scuffed wide in another off-target first half from the hosts but Newcastle were far from their energetic best, with the toll of their recent run of games and injuries seemingly affecting the visitors. Miguel Almiron miscued a good opening from Joelinton's pass and Alexander Isak nodded just wide before the break.
Calvert-Lewin again made contact close to goal at the start of the second half and again failed to find the right connection when his glancing header deflected off Newcastle defender Jamaal Lascelles and forced Dubravka to prevent an own goal.
Gordon heard the boos turn to ironic cheers from the Everton supporters when his shot flew high and wide from 25 yards - but he should have silenced them when he pick-pocketed Tarkowski only to shoot straight at Jordan Pickford. The Everton keeper later needed treatment after appearing to pull a muscle kicking the ball but played on to the final whistle.
Gordon again shot over soon after from a break, following good work by Isak, and instead it was Everton who punished Newcastle's misses. Trippier was caught in two minds and lost control of the ball, allowing McNeil to canter away and score for a second game in a row. It's the first time he's done that since March 2019.
Incredibly, Trippier made a near-identical mistake moments later which handed the chance for Harrison to tee up Doucoure. It was game over at that point for a Newcastle side out on their feet and Beto rubbed salt in the wounds after a pass through from Nathan Patterson. A night to remember for Beto and a big one for Everton but Newcastle are in desperate need of a breather.
Dyche: We've been in terrific form
Everton boss Sean Dyche to Amazon Prime: "This season, apart from the obvious with the 10 points, I think we've been in terrific form. We talked about continuing performances and continuing to believe in scoring goals.
"There have been other performances here which have been better than that and we couldn't get a win. That's the madness of football. At half-time, I said: 'You've had a really strong half but you have to keep doing it.' To regrip the game with our performance was very pleasing for me. Last season, these games were getting away. Now, we're gripping them."
Howe: We didn't stamp our authority on the game
Newcastle boss Eddie Howe to Amazon Prime: "It was a tough night in the end. I thought the first half was very even, a scrappy game - probably what we thought it would be. I don't think we stamped our authority enough on the game in those early stages. I thought we had our best spell in the second half, when we camped them in for 15, 20 minutes, but we weren't clinical enough when those chances came. We shot ourselves in the foot, really.
"Trippier's been absolutely magnificent. He's probably been the catalyst behind what we've done. As a team, we weren't where we needed to be - that's why we didn't win the game."
What's next?
Everton are back at Goodson Park on Sunday as they host Chelsea in the Premier League, kick-off 2pm. They will then be live on Sky Sports on Saturday December 16, taking on Burnley on Saturday Night Football, kick-off 5.30pm.
Newcastle are back on Sky Sports on Super Sunday as they take on Tottenham in the Premier League, kick-off 4.30pm. They will then play their final Champions League group-stage game at home to AC Milan on Wednesday December 13.