They remain fifth - a point behind the Gunners, with both clubs having four more games to go - after they were undone by a Palace side who were worthy victors of an absorbing contest.
The result, Everton's first home loss since Boxing Day and only their second all season, brought their seven-match top-flight winning streak to an end.
Palace's own run of victories, meanwhile, extended to four games as they moved up to 11th, on to 40 points - the total widely regarded as a guarantee of safety - and 10 points clear of the relegation zone, with four more fixtures left.
Tony Pulis' men deservedly went in at half-time with a 1-0 lead thanks to Jason Puncheon's strike from Marouane Chamakh's assist in the 23rd minute - his fourth goal in the past three matches - after Tim Howard had parried a cross from Yannick Bolasie.
The dangerous Bolasie then provided the corner from which Scott Dann sent a free header past Howard four minutes after the interval to make it 2-0.
Substitute Steven Naismith reduced the deficit with a close-range finish in the 61st minute, but Cameron Jerome restored Palace's two-goal cushion in the 73rd.
Kevin Mirallas' effort with four minutes of normal time remaining then set up a nervy finale which Palace managed to come through with their lead intact and another vital three points secured.
Source : PA
Source: PA