Jason Puncheon had the Eagles’ best chance of the game, racing through on goal from a Mile Jedinak pass – only to be thwarted by Joel Robles in the Everton goal.
Ross Barkley came closest for the Toffees, bending a superb effort around Wayne Hennessey but the ball crashed off the underside of the crossbar and into the grateful hands of the Welsh goalkeeper.
Roberto Martinez’ side had to withstand heavy pressure from Palace throughout the game, particularly after James McCarthy was shown a second yellow card midway through the second-half and was subsequently sent off.
Palace edge first-half
Alan Pardew made just one change to the side that beat Norwich City on Saturday; Wilfried Zaha returned to the side following his cameo appearance against the Canaries and replaced Bakary Sako. Dwight Gayle kept his place up front despite the return of Connor Wickham and Emmanuel Adebayor – who both had to settle for places on the bench.
Palace were by far the better side in the early exchanges and produced the first two chances of the game: Zaha’s direct run took him past McCarthy before he squared the ball to Gayle who sliced his effort just wide.
Zaha then had a chance of his own, taking advantage of a sloppy Ramiro Funes Mori clearance but the winger’s eventual effort flew just over the bar.
Due to their attacking approach, Pardew’s side were always risking an Everton counter-attack, and the toffees almost went ahead from a quick break when Barkley dribbled forward but saw his shot excellently blocked by Damien Delaney.
Barkley’s chance gave Everton a restored sense of confidence and they endured their best spell of the game midway through the first-half. The Toffees’ best chance of the first period fell to Seamus Coleman who had not been tracked at the far post from a cross and volleyed towards goal but Hennessey was equal to the goal-bound effort.
An exciting first-half culminated with a fantastic piece of skill from Gayle, watching a ball go over his shoulder before executing an overhead kick that was ever so unlucky not to nestle in the corner of Joel’s goal.
Gayle was replaced at half-time – presumably because of an injury – by Wickham as Palace continued their good form into the second-half.
McCarthy red card hands initiative to Palace - who fail to frustratingly capitalise
However, it was Barkley who almost gave his side the lead when he received a pass from Romelu Lukaku before crashing a shot goalwards, but only the underside of the crossbar denied him from what would have been a sensational goal.
The game fell further into Palace’s favour soon, however, when McCarthy cynically blocked Yannick Bolasie’s run and referee Mike Jones had no hesitation in producing a second yellow card having already booked the midfielder for a similar foul early in the first-half.
Pardew sent on Adebayor in search of a winning goal, but a host of missed chances followed, with Wickham and Adebayor very much the guilty suspects of some poor finishing.
The former Sunderland striker had Palace’s best chance in the final stages, leaping above John Stones to head towards goal, but the ball missed the right-hand post by inches.
Palace will certainly feel the result is two points dropped rather than a point gained, however, had Pardew and his side been offered a draw pre-match, they would definitely have accepted it.