Crystal Palace substitute Michy Batshuayi scored a late equaliser to put a significant dent in Everton's hopes of playing European football as the sides drew 1-1.
Hosts Everton missed chances in the first half before playmaker James Rodriguez marked his return to the side with his 100th goal in European club football in the 56th minute.
But Palace's on-loan Chelsea striker Batshuayi converted an angled drive four minutes from time and moments after coming off the bench, to leave Carlo Ancelotti's side regretting missed opportunities.
Everton still have a game in hand on all of their rivals chasing the top four spots but this was a match the Italian suggested they had to win to maintain the pressure.
It means they stay in eighth and remain outsiders in a tight race in which any failure to capitalise on opportunities will be costly.
The bank holiday looked like a good one for them after Rodriguez, absent for six weeks as the club sought to rectify a niggling calf problem, made the breakthrough.
In squeezing a shot inside the unsighted Vicente Guaita's left-hand post, the Colombia international scored Everton's first second-half Premier League goal since the Merseyside derby in mid-October.
They had failed with 51 attempts in 11 matches.
Rodriguez has chalked up five goals and three assists in nine Premier League starts at Goodison this season.
He could well be the key to their success, with Richarlison and Dominic Calvert-Lewin misfiring.
Rodriguez may have missed five matches but Everton had won only two and came into this game after three successive defeats in all competitions.
His goal, when it eventually came, was not the sweetest of strikes but finished off a move in which left wing-back Lucas Digne's cross was turned goalwards by substitute Gylfi Sigurdsson.
It was saved by Guaita but returned into the danger area by the Toffees' other wing-back, Seamus Coleman, for the Colombian 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 Eberechi Eze, from distance, and Wilfried Zaha forced Robin Olsen to make saves.
But it was Batshuayi, who on recent international duty with Belgium 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.
That is likely to be their Achilles' heel at this stage of the season, when results mean more than performances.
It will be even more frustrating after a first half lacking in quality up front, with Richarlison particularly at fault.
The Brazil international could have had a hat-trick but the fortnight's break for internationals, in which he was not involved, appeared to have dulled his senses.
Richarlison twice headed over, shot at Guaita and inexplicably tried to square a pass to Calvert-Lewin as he bore down on goal, although a delayed offside flag spared his blush.
His frustrations showed in a free kick shortly before half-time when, having been the player fouled, he refused to defer to regular specialists Sigurdsson, Digne or Rodriguez despite the pleadings of Digne, and fired wide.
Calvert-Lewin also seemed to be adversely affected despite two goals for England against San Marino, as he also failed to beat Guaita one-on-one when he charged to the edge of his area.
Andre Gomes had created the most chances from deep but his replacement by Sigurdsson just past the half-hour meant all of Ancelotti's first-choice midfield is now injured.
"The reason was we were not able to kill the game when we had the opportunity," Ancelotti said.
"We had a lot of chances and usually in the last games our strikers in those situations were really clinical. Tonight they needed 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 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."
During the international break Batshuayi, while away with Belgium, had said he had the trust of his country but not his club.
Palace boss Roy Hodgson said Batshuayi's attitude since returning had been good and that had given him the faith to use him, even if it was as an 84th-minute substitute.
"He scored a goal, which was important. He has to be very pleased with that and we are pleased with it," Hodgson said.
"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."
