Everton pulled a goal back just after the hour mark when Steven Naismith bundled the ball over the line from close range, but Palace's two-goal lead was restored in the 73rd minute as Cameron Jerome fired into the bottom corner.
The hosts did get another goal back with five minutes remaining thanks to a smart finish from Kevin Mirallas, but they couldn't provide any additional late drama as Palace held out for the win.
Here, Sports Mole takes an in-depth look at a costly evening for Everton.
On target: 5
On target: 4
Was the result fair?
A draw would have been the fairest result in tonight's match, but once again Palace triumphed tactically and executed their gameplan to perfection to pick up all three points. They soaked up plenty of Everton pressure before hitting the hosts on the break on a number of occasions.
The Eagles deserved their lead at half time, but Everton were better in the second half and asked a lot more questions of the defence. They were very much on top from the moment they scored their first goal, with Jerome's strike coming against the run of play.
It is no surprise to see Everton dominate the statistics, but that does not mean that they should have won this game. Palace's tactics meant that they were never going to have anywhere near as much of the ball as Everton, but they played their own game expertly.
Roberto Martinez would have taken a repeat of his side's last outing, in which they were lucky to win against Sunderland after a below-par performance. Instead, he got a decent performance overall but one that was not enough to get them anything from the game.
Everton controlled possession for large periods of the game, but they lacked any cutting edge against a Palace defence as stubborn as ever. They were by no means at their best, and it was hard to see them finding a way back into the game at 2-0 down.
However, they did improve after their opening goal and carved out enough chances to have completed the comeback in the end. Palace's third goal came at a time when Everton were on top and looking for an equaliser, and that was a killer blow for them.
In the end, the Toffees were not as solid as usual in defence, while they failed to take full advantage of the few chances afforded to them by Palace.
Once again, it was a Tony Pulis special for Palace tonight. His organisation of the defence has completed transformed the team and Everton are not alone in having struggled to break them down this season.
The visitors soaked up plenty of pressure and defended really well, despite allowing Everton more chances than they usually allow teams. Crucially, they were clinical at the other end too, and that is something that has been lacking for the Eagles this season.
The win was certainly unexpected but is testament to the work that Pulis has done since taking charge of the team. A four-match winning streak has taken them away from danger and they now sit on the magic 40-point mark, safe from relegation.
Sports Mole's man of the match
Jason Puncheon: It was a choice between Jason Puncheon and Yannick Bolasie for this award, and the former just about gets it due to his role in two of the goals. In addition to scoring the first with a composed finish, he also did really well to set up Jerome for the killer third goal, cutting inside before biding his time and sliding an accurate pass to his striker.
Bolasie does deserve an in-depth mention, however, as he tore Everton apart at times in the first half. It was his work down the right channel that ultimately gave Puncheon the chance to score, while his corner also picked out Scott Dann for Palace's second.
It was a relatively gaffe-free game today, but Tim Howard will certainly have felt that he could have done better with the opening goal. Leighton Baines will also not be happy with his contribution as Bolasie burst past him and into the box far too easily, but Howard then proceeded to push the ball out into a dangerous area that led to Puncheon tucking it home.
Andre Marriner had a quiet game tonight. There were one or two half-hearted appeals for penalties throughout the match, but on each occasion Marriner gave them little thought and he was right to do so. There were no major moments, and he can be happy with a pretty solid performance.
Everton: Everton will need to pick themselves up quickly after this one as they face Manchester United at Goodison Park on Sunday.
Crystal Palace: Palace, meanwhile, will be looking to make it five wins in a row against West Ham United at Upton Park on Saturday.