Scott Dann headed in Eze’s corner to put the hosts in front on 12 minutes.
Palace doubled their lead 10 minutes later with Eze's first Premier League goal, a curling free-kick.
Patrick Bamford, who had an earlier effort overturned by the VAR for offside, pulled a goal back in the 27th minute, volleying in Mateusz Klich’s pass.
Palace restored their two-goal lead three minutes before half-time when Patrick van Aanholt’s cross was deflected in by Helder Costa.
Jordan Ayew converted Wilfried Zaha’s pass to secure the win on 70 minutes.
Palace move up to seventh with 13 points, while back-to-back defeats drop Leeds to 15th on 10 points.
Budweiser King of the Match: Wilfried Zaha (CRY)
Crystal Palace: 21 Nov v Burnley (A)
Leeds: 22 Nov v Arsenal (H)