Palace's winning run came unstuck against the Toffess as Romelu Lukaku's goal just two minutes into the game proved to be enough to give Everton the victory.
The Belgian hitman scrambled the ball home early on in a placid match that saw plenty of endeavour from the home side who ultimately couldn't find a way past the Everton defence who cleared off their own goalline twice inside the opening 10 minutes.
The defeat ends Alan Pardew's winning start to life in the Eagles' hotseat at four wins, but handed Roberto Martinez's side a first win in nine outings.
The key moment came just two minutes in as Palace fell behind early on once again. Steven Naismith managed to get in behind the hosts' backline down the right and his low cross was parried by Julian Speroni into the path of Lukaku who bundled the ball in.
But having gained more points than any other side in the league this season from losing positions Palace's weren't to be deterred and went inches from equalising twice a couple of minutes later.
A corner into the box wasn't effectively cleared and Yaya Sanogo saw a shot blocked on the line by John Stones, before Dwight Gayle beat Joel Robles to the ball and hooked it towards goal but Phil Jagielka managed to get back in the nick of time to acrobatically hoof the ball to danger – the goalline decision system showing the ball was millimetres from crossing the whitewash.
The in-form striker then saw a bicycle kick clear the crossbar before Marouane Chamkah headed tamely wide from a good position, and another player in decent form of late Jason Puncheon showed his confidence in collecting the ball 40 yards from goal, taking a couple of touches and letting fly from distance but Robles did well to beat away his low effort on 35 minutes.
The winger then screwed a volley over the top when Gayle won a flick-on in first-half stoppage time but the Eagles, who had seen Chamakh depart the field with a suspected broken nose and debutant Jordon Mutch replace him, went in trailing at the break.
The second half began in a lacklustre fashion with Palace enjoying plenty of possession in the Everton half but unable to carve out a decent opportunity, and only got the crowd excited when Gayle blazed over from long range around the hour mark.
Everton could have sealed the win when a low ball by Muhamed Besic flashed across the face of Speroni's goal and narrowly avoided Lukaku, and with five minutes to go Aiden McGeady dispossessed Puncheon in the Eagles' box and took aim for the top corner but Speroni managed to push the ball away from goal.
Having scored once already, the Belgian was hungry for more and after being released by Naismith he fired the ball into the side-netting, before McGeady squandered a good opportunity in injury-time when he thumped the ball over from a tight angle with teammates in better positions, but just the one goal would be enough for the visitors to end Palace's great start to 2015.
Palace: Speroni, Ward, Dann, Delaney, Kelly (Zaha 66), Puncheon, McArthur, Ledley, Gayle, Chamakh (Mutch 25), Sanogo (Murray 71). Subs not used: Hennessey, Mariappa, Hangeland, Campbell.
Everton: Robles, Baines, Jagielka, Stones, Coleman, Besic, Barry, McGeady, Mirallas (Oviedo 68), Naismith, Lukaku (Kone 90). Subs not used: Griffiths, Distin, Alcaraz, Gibson, Barkley.