Scott Dann netted on Merseyside for the third time in Palace’s last four trips to Liverpool, but they would ultimately have to settle for a point against Everton.
The centre-back headed in a Jason Puncheon corner on 75 minutes to give Alan Pardew’s side the lead, but five minutes later Romelu Lukaku equalised to earn the Toffees a draw.
The home side extraordinarily hit the woodwork three times during the game, but Palace held firm to once again move into the top six of the Premier League table.
An entertaining game began with plenty of goalmouth action with Connor Wickham barging his way forward and forcing Tim Howard into an early low save, and Ross Barkley played a one-two with Lukaku on the edge of the area but fired a first-time curler over.
Wickham was unlucky not to get his Eagles account up and running on 15 minutes. After a corner went straight through the penalty area, Yannick Bolasie picked up the loose ball, skinned Brendan Galloway by slipping the ball through his legs and crossing for the Palace attacker who headed powerfully towards goal, but Howard managed to block the attempt with his chest.
However it was the Toffees fans who were next to be rueing a near miss just five minutes later. Lukaku gained possession 30 yards from goal and bundled his way past a couple of Eagles defenders before aiming for the bottom corner, but watched the ball thud against the base of the far post.
Soon after Arouna Kone put a shot into the home fans sat behind the goal but the Eagles managed to snuff out any Everton momentum following those dangerous moments. In the meantime they could only muster some wayward shooting of their own from Bolasie, James McArthur and Yohan Cabaye as an even half drew to a close.
After the resumption the hosts found themselves in the ascendancy and Kone curled off target before Barkley nonchalantly headed narrowly wide.Once again Palace responded and Bolasie embarked on a powerful run through the middle of the park on the counter, teased his way past John Stones and forced Howard to save with his legs.
At the other end Wayne Hennessey’s goal seemed to be living a charmed life and just before the hour mark his woodwork was rattled again. Barkley swung in a free-kick that Wickham inadvertently flicked on, but breathed a huge sigh of relief when it hit the bar and bounced the right side of the line from an away perspective.
The Welsh keeper was then forced to make his first save in fine style when Lukaku held the ball up and laid it off to Tom Cleverley who arrowed a thunderous shot towards the top corner but Hennessey used every inch of his 6’6’’ frame to get the slightest of fingertips to the ball and divert it over.
Despite being up against it, Pardew’s men still look dangerous on the counter and Jason Puncheon who forced Howard into a good save of his own after a sweeping move from the back, and from the resulting corner Palace took the lead. Puncheon swung it in and Dann climbing highest to once again head in on Merseyside.
Minutes later the Palace goalframe was struck again when Gareth Barry found Lukaku who hit a shot on the turn that went over Hennessey and smacked the crossbar while narrowly avoiding going in off the keeper, but the Belgian powerhouse wasn’t to be denied.
10 minutes from time the resistance was broken when Gerard Deulofeu got the ball on the byline and slid it across the face of goal where Lukaku was on hand to nudge it over the line from a couple of yards out tp score his third goal in his last three outings against Palace.
Late on Jordon Mutch fired wide of the mark as the visitors once again charged forward, and in the dying seconds Kone shanked an effort wide but the Eagles’ good run on Merseyside would continue.
Everton: Howard, Coleman, Funes Mori, Stones, Galloway (Baines 63), Barry, Cleverley, Deulofeou, Barkley, Kone, Lukaku. Subs not used: Robles, Gibson, Osman, Mirallas, Lennon, Naismith.
Palace: Hennessey, Ward, Dann, Delaney, Souare, Cabaye (Mutch 77), Jedinak, Bolasie, McArthur, Puncheon, Wickham (Gayle 77). Subs not used: Speroni, Kelly, Bamford, Campbell, Chamakh.