Match ends, Crystal Palace 0, Everton 0.
Crystal Palace could not record back-to-back wins for the first time since December as 10-man Everton held out for a draw at Selhurst Park.
James McCarthy was sent off for fouls on Yohan Cabaye and Yannick Bolasie, and Toffees keeper Joel Robles did well to keep out Jason Puncheon's effort.
Everton - winless in five league games - struck the bar with a fine Ross Barkley strike before the dismissal.
They defended resolutely late on and have 40 points, two more than Palace.
Both Palace and Everton have a comfortable cushion on Sunderland - who sit in the final relegation place on 27 points - but the stalemate will do little to lift scrutiny of their worrying form.
Ten-man Everton stand tall
The Toffees showed application in sticking to their task after losing midfielder McCarthy, who had completed 100% of his 28 passes before the red card on 52 minutes.
Robles made six saves in all but deserved credit for his stop at the feet of Puncheon, who had time and space and could have scored for the second successive game.
However, it was Barkley's rasping 20-yard drive off the crossbar that was easily the closest anyone came to breaking the deadlock.
Everton boss Roberto Martinez - a subject of criticism from sections of the club's fanbase - was undoubtedly more pleased than his opposite number Alan Pardew.
"It was a more than decent result," said Martinez. "The resilience and hard work, and to be able to be so solid, was great.
"We had as many chances. Joel Robles had to be at his best but it was a level game. To play like that with 10 men, it was incredibly satisfying."
'Wow...we should have won that'
Palace struggled to carve the visitors open, despite their one-man advantage, and boss Pardew admitted himself that he expects more from his forwards.
Dwight Gayle attempted an audacious overhead kick in the first half which went just wide of the post, while Emmanuel Adebayor - on as a second-half substitute - looked lively in the box but lacked the killer touch.
Palace earned their first league win since December on Saturday against Norwich, and Pardew said: "I would have taken four points from these last two games... but wow, we should have won that.
"Although I'm frustrated, I'm pleased with another good performance. I want my offensive players to be a bit hotter, but I'm pleased with two clean sheets."
Man of the match - Seamus Coleman
The stats you need to know
- James McCarthy was shown his first Premier League red card in his 201st game in the competition.
- Everton have now been shown 83 red cards in Premier League history - at least two more than any other side.
- After 12 games without a clean sheet in 2016, Crystal Palace have now not conceded in their last two Premier League fixtures.
- The Toffees have scored just one goal in their last four Premier League games.
Everton host Southampton on Saturday, while Crystal Palace travel to Arsenal on Sunday.
- 11ZahaSubstituted forSakoat 77'minutes
- 10BolasieSubstituted forAdebayorat 66'minutes
- 16GayleSubstituted forWickhamat 45'minutes
- 25Funes Mori
- 16McCarthyBooked at 52mins
- 18BarryBooked at 90mins
- 9KonéSubstituted forBesicat 54'minutes
- 20BarkleySubstituted forMirallasat 86'minutes
- 12LennonSubstituted forOviedoat 69'minutes
- Mike Jones
- Shots on Target
Second Half ends, Crystal Palace 0, Everton 0.
Gareth Barry (Everton) is shown the yellow card for a bad foul.
Yohan Cabaye (Crystal Palace) wins a free kick in the attacking half.
Foul by Gareth Barry (Everton).
Attempt blocked. Jason Puncheon (Crystal Palace) right footed shot from outside the box is blocked.
Attempt missed. Emmanuel Adebayor (Crystal Palace) header from the left side of the six yard box is close, but misses the top left corner. Assisted by Jason Puncheon with a cross.
Substitution, Everton. Kevin Mirallas replaces Ross Barkley.
Corner, Crystal Palace. Conceded by Seamus Coleman.
Attempt saved. Ramiro Funes Mori (Everton) left footed shot from outside the box is saved in the top centre of the goal.
Foul by Emmanuel Adebayor (Crystal Palace).
Gareth Barry (Everton) wins a free kick in the attacking half.
Attempt missed. Connor Wickham (Crystal Palace) header from the centre of the box is too high. Assisted by Bakary Sako with a cross.
Foul by Jason Puncheon (Crystal Palace).
John Stones (Everton) wins a free kick in the defensive half.
Corner, Everton. Conceded by Scott Dann.
Substitution, Crystal Palace. Bakary Sako replaces Wilfried Zaha.
Foul by Yohan Cabaye (Crystal Palace).
Leighton Baines (Everton) wins a free kick in the defensive half.
Corner, Crystal Palace. Conceded by Muhamed Besic.