Oliver Glasner watched on from the stands as Crystal Palace were held to a 1-1 draw with Everton at Goodison Park after Amadou Onana scored late to cancel out Jordan Ayew's opener.
The new Palace boss, announced ahead of kick-off as it was confirmed that Roy Hodgson was stepping down, witnessed a nervy encounter between two relegation-threatened sides, which appeared close to being settled by a moment of solo quality from Ayew.
Jean-Philippe Mateta held the ball up brilliantly for Ayew in the 66th minute, before the Ghana international rifled the ball across Jordan Pickford into the far corner.
The twist, in a relatively nondescript encounter, came late, but importantly for the hosts - winless in eight games - it came.
Dominic Calvert-Lewin missed a pair of decent chances either side of the break, before substitute Onana made the breakthrough the Goodison crowd craved by heading Dwight McNeil's corner home at the back post six minutes from time.
Everton climb out of the bottom three as a result, but remain level on points with 18th-placed Luton Town, who have played a game less, while Palace are five points better off in 15th.
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How Onana rescued draw for Everton
In a week that Everton are expecting to learn their fate, an independent panel deciding whether their 10-point deduction is just punishment for breaching Profit and Sustainability rules, it was an unfamiliar scorer who rescued a valuable point.
McNeil had been teasing the ball into the box all night, many of them landing on the head of wasteful Calvert-Lewin, who has amassed the highest xG (2.16) of any player who is yet to score a league goal in 2024.
The delivery that counted came from a corner, which was met by a towering Onana leap, and he squeezed the ball beyond Sam Johnstone to snatch the point which lifted the Toffees out of the bottom three - for now at least.
Defeat would have been disastrous for Dyche's side but the draw at least ensured Palace, with just two league wins in their last 14 matches, were denied a victory which would have pulled them eight points clear of the relegation zone.
Assistant managers Paddy McCarthy and Ray Lewington took charge of the game for the visitors, while Hodgson's successor Glasner got his first taste of what life will be like at Palace, and can take some encouragement from a spirited display without the stardust of injured duo Eberechi Eze and Michael Olise.
The home side, however, might well feel this was an opportunity missed. Dyche said post-match "we were constantly asking questions," but his side were far from their best, and careless in front of goal - this is their longest winless run since Frank Lampard was in charge.
Calvert-Lewin was culpable with headers in either half from McNeil crosses, which he would have buried at the height of his powers but an obvious lack of assurance and belief stretches his goalless run to 19 games.
Carra: 45 minutes of 'Everton' football not enough
Sky Sports' Jamie Carragher on Monday Night Football:
"Yes, this puts Everton outside the bottom three but it will still feel like two points dropped and a disappointment.
"But Everton were much better in the second half, and that's what I'd call Everton football. On the front foot, putting crosses in, and making Goodison Park an atmosphere and fortress.
"They have to do that for 90 minutes, 45 is not enough."
McCarthy: Glasner watched a team with spirit
Crystal Palace assistant manager Paddy McCarthy:
"It was a wonderful goal by Jordan, unfortunately we couldn't hold out in the end. We knew they would pose us some questions from set-plays and we just didn't answer them until the end. We're disappointed with conceding the goal through a set-piece, but we're ultimately happy with a point and move on.
"There's lots of quality in the squad, [Glasner] is coming into a squad with a lot of character and spirit like they showed today. Lots of positives I'm sure he's seen when he was looking down on the team today.
"I can't say whether [having clarity] helped the players or not, but I'm sure they were aware he was watching on. The prep was all done before we were aware of his appointment, but the players are professional - the way they set about things, they deserve a lot of credit."
Dyche: We have to meet Goodison expectations
Everton manager Sean Dyche:
"Second half I was [happy]. First half, to be fair to the players, there's a new manager sitting in the stands and we know how that often works. Fair play to Palace, it worked in their favour and they had that edge about them in the first half.
"Second half they found a goal out of a nothing moment, and we reacted very well to that.
"I thought we were on the front foot, asking questions, we were making chances from general play and looked a threat from set-pieces.
"Sometimes, it's a different mentality. The hardest fight to win is the one everyone thinks you should. We've got to grow with that, and I know in my short time here the crowd here expect a lot, and we have to grow towards that.
"It's another point on the board and we've just popped out of the relegation zone but there were chances - we've got to start taking them. There were a couple of golden chances we didn't take."
Opta: Set-piece prowess digs Everton out of trouble
- Everton have scored 10 goals in the Premier League this season from corners - only Arsenal (11) have scored more via corners.
- Crystal Palace have now gone 14 Premier League matches without a clean sheet - the longest ongoing run of any current top-flight side.
- All three of Amadou Onana's Premier League goals for Everton have been headers from corners - his last two have also both been assisted by Dwight McNeil.
What's next?
Everton are back in Premier League action on Saturday as they travel to Brighton; kick-off 3pm.
Crystal Palace also play again on February 24 as they host Burnley; kick-off 3pm.
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