Everton were seeking to return to the Champions League places after Arsenal had leapfrogged them by beating West Ham United on Tuesday, but instead they remain in fifth place, a point behind Arsene Wenger's side with four matches to play.

Palace went 2-0 up through goals from Jason Puncheon and Scott Dann either side of half-time, with Cameron Jerome adding a third in the 73rd minute after substitute Steven Naismith had reduced the arrears for the hosts.

Kevin Mirallas clawed a goal back for Everton with four minutes left, but Tony Pulis's Palace would not be denied a victory that took them to the 40-point mark that usually represents safety from relegation.

Palace have now won five consecutive games and are almost certain to avoid the drop, having been bottom of the table, six points from safety, when Pulis succeeded Ian Holloway as manager in late November.

Everton manager Roberto Martinez made three changes to his starting XI at Goodison Park, with Gareth Barry the only recognised holding midfielder, and his side made a bright start to the game.

Barry headed over from an early Aiden McGeady corner, while Ross Barkley had a penalty appeal waved away after tumbling over Joe Ledley's outstretched leg and McGeady shot wide from 25 yards.

Palace succeeded in keeping the hosts at arm's length, however, and in the 23rd minute they took the lead.

Yannick Bolaise cruised past Leighton Baines on the Palace right and although his cross was palmed away by Tim Howard, Marouane Chamakh teed up Puncheon to sweep home his fourth goal in as many matches.

Eager to capitalise on their momentum, Palace continued to press forward, and Bolasie saw a low shot come back off the post 10 minutes before half-time, with Jerome prodding the rebound wide.

- Everton changes reap rewards -

In response, Romelu Lukaku drew a sharp near-post save from Palace goalkeeper Julian Speroni, but the visitors finished the half in the ascendancy, with the livewire Bolasie cutting in and shooting over.

Martinez made a change at half-time, sending on Naismith in place of Gerard Deulofeu, but within minutes of the restart the home side were two goals down.

After Ledley had forced Howard into a save at his near post, a corner from Bolasie picked out the unmarked Dann, who had the simple task of heading home from seven yards.

McGeady drilled narrowly wide as Everton sought an immediate reply, while Lukaku put a header wide from a Baines free-kick.

Martinez reacted by making a double substitution, sending on Ross McCarthy and Leon Osman for McGeady and Barry, and the changes reaped immediate dividends.

Mirallas put a cross into the Palace box from the right and after Baines headed the ball back across goal from the left, Naismith tapped home.

Gradually, Palace were forced back, with a stretching Mirallas putting a Baines cross just over from close range and Speroni tipping a shot from Osman onto the bar.

It was Palace who struck next, however, with Jerome gathering a pass from Puncheon and drilling a low shot into the bottom corner.

After Speroni blocked from Barkley, Mirallas reduced the arrears in the 86th minute, clipping home from Barkley's deflected pass.

The Belgian could not repeat the trick in injury time, however, missing his kick after Barkley's pass gave him a clear sight of goal, as Palace held on for an impressive victory.