Michy Batshuayi came off the bench to deliver a blow to Everton's European hopes as his equaliser grabbed Crystal Palace a 1-1 draw.
Carlo Ancelotti's team looked set to move level on points with Tottenham in fifth when James Rodriguez - making his first start since the win at Liverpool - found a way past Crystal Palace goalkeeper Vicente Guaita, who was in inspired form in denying Dominic Calvert-Lewin and Richarlison.
However, Batshuayi, who had last week accused Roy Hodgson of not trusting him amid a lack of game-time this season, was on hand to level the game with just four minutes remaining.
This latest setback means they have won just one of their last eight home Premier League home games as their form at Goodison Park continues to hold them back.
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The result leaves Ancelotti's side in eighth place, two points behind Tottenham in fifth, albeit they have a game in hand.
Everton: Olsen (6), Coleman (7), Holgate (7), Keane (6), Mina (7), Digne (7), Davies (6), Andre Gomes (6), James (7), Calvert-Lewin (7), Richarlison (7)
Subs: Sigurdsson (7), Godfrey (6), Gbamin (6)
Palace: Guaita (8), Ward (6), Kouyate (6), Cahill (6), Van Aanholt (6), Ayew (6), Milivojevic (5), Riedewald (5), Eze (7), Benteke (6), Zaha (6)
Subs: Batshuayi (8), Mateta (6), Schlupp (7)
Man of the match: Vicente Guaita
How Everton threw away golden opportunity...
Ancelotti had won five of his six managerial meetings against Hodgson, all in the Premier League, and both shared a big embrace in the pre-match pleasantries. It would have been Hodgson the happier in the early stages as his team restricted Everton possession but never really looked likely to find a way through themselves. Eberechi Eze tested Robin Olsen from an angle but that was as good as it got.
Everton then took charge and created three big chances in a matter of minutes. Calvert-Lewin seized upon an incredible through ball from Mason Holgate but Guaita narrowed the gap and blocked it away and Richarlison headed over from a Seamus Coleman cross seconds later.
- Carlo Ancelotti made four changes from the FA Cup defeat to Manchester City. Allan, Ben Godfrey, Gylfi Sigurdsson and Joao Virginia made way for Michael Keane, James Rodriguez, Tom Davies and Robert Olsen.
- Roy Hodgson named the same XI that saw off West Brom. Wilfried Zaha and Christian Benteke played as a front two.
Richarlison - who cut a frustrated figure - scampered through past Gary Cahill on 22 minutes but Guaita read his finish into the far corner.
Perhaps riled by not finding the net, Richarlison then grabbed the ball from a set-piece about 22 yards out and seemed to go against team orders for Lucas Digne to have a strike. His effort was off target and his team-mates did not look impressed with his shenanigans.
The goal eventually came just after the break. Left wing-back Digne's cross was turned goalwards by substitute Gylfi Sigurdsson but his effort was saved by Guaita. However, Coleman was alive to the loose ball and returned it into the danger area for James to thread a shot around a crowd of legs.
It finally sparked Palace, still without a win in 13 meetings with the Toffees, into life after almost an hour of containment, and Eze, from distance, and Wilfried Zaha both forced Olsen to make saves.
But it was Batshuayi, who on recent international duty with Belgium had said he had the trust of his country but not his club, who struck within two minutes of coming on to make it just one victory in eight home league matches for Everton.
Calvert-Lewin had a late chance to win it for Everton but despite two goals for England against San Marino, his confidence looked low he also failed to beat the brilliant Guaita one-on-one as he charged to the edge of his area.
Man of the match: Vicente Guaita
Sure, Everton's finishing was very wayward but the Palace goalkeeper's positioning and shot-stopping ability was first class as he made six saves across the 90 minutes. Calvert-Lewin especially will be very disappointed he could not get the better of the Spanish goalkeeper as a player of his international standing should have finished one of his two chances.
Has there been a better value for money free signing in Premier League history than Guaita? I would argue not.
What the managers said...
Carlo Ancelotti said: "The reason (for the result) was we were not able to kill the game when we had the opportunity.
"We had a lot of chances and usually in the last games our strikers in those situations were really clinical. Tonight they need to do better.
"After we opened the scoring we had opportunities, we could have closed the game, and sometimes it can happen the last 10 minutes you have to defend and there might be a little mistake.
"That's what happened in the last situation and and we have two points less. We deserved to win, we have lost points for our mistakes. We were not unlucky, I have to say.
"I think the position in Europe is still there because we are in the fight and we have one game in hand but we have to be more focused in this situation - when you deserve to win, you have to win."
Roy Hodgson said: "Batshuayi scored a goal, which was important. He has to be very pleased with that and we are pleased with it.
"When players go on international duty and they've just scored a goal for their national team and they are asked how it is at Palace as they are not playing a lot, it would be a surprise to me if he didn't make the comments he did.
"Since he came back he has been in good spirits and contributed well in training sessions, which has given me the faith to put him on tonight to see what he could do for us and luckily he has repaid that faith.
"It is good for me to know, going forward, Michy still has goals in him."
- Crystal Palace have suffered just one defeat in their last six Premier League games (W2 D3) after losing four of the six before that.
- Everton mustered 15 shots in the game, only managing more in a league game this season once before, against West Brom in September (17).
- Crystal Palace have kept just one clean sheet in their last 19 Premier League away games (W5 D3 L11), with that coming in a goalless draw at Arsenal in January. Only Sheffield United (0) have kept fewer clean sheets on the road than the Eagles this season.
- Everton captain Seamus Coleman has been directly involved in three Premier League goals against Crystal Palace (including two assists this season), only registering more against Manchester City (4).
- Jean-Philippe Gbamin made just his third Premier League appearance for Everton, and his first in 597 days since August 2019 v Watford (his first appearance also came v Crystal Palace in August 2019).
Everton are once again in action on Monday Night Football next week when they visit Brighton (8.15 kick-off). Meanwhile, Palace welcome Chelsea next Saturday, live on Sky Sports (5.30 kick-off).