The Senegal forward got to the milestone at Anfield by converting from close range in the 43rd minute after Mohamed Salah´s header from a corner was parried out by Palace goalkeeper Vicente Guaita.
Browsing: Vicente Guaita
The visitors created the better opportunities at Selhurst Park with the majority falling to centre-back Joachim Andersen, although Josh Maja was brilliantly denied by Vicente Guaita from close range in the second half.
Eze kick-started January with his Premier League Goal of the Month-nominated strike against Sheffield United and rounded it up with his fizzing effort against Wolverhampton Wanderers.
Wolves had knocked Palace out of the cup by the same scoreline when they met earlier this month.
While Roy Hodgson’s men managed to take a point from their clash with Leicester, Sheffield United’s abysmal run continued with a narrow defeat to fellow strugglers Burnley in midweek.
The tone was set inside three minutes when Takumi Minamino scored his first Premier League goal, slotting home after some good work from Sadio Mane.