Palace, who lost Wilfried Zaha to an early injury, went behind on 23 minutes when Trent Alexander-Arnold curled in a brilliant free-kick.
Mohamed Salah converted Fabinho's pass over the Palace defence a minute before half-time to put Liverpool 2-0 ahead.
Fabinho then added a third at Anfield on 55 minutes with a spectacular strike from 30 yards out.
Sadio Mane put Liverpool further ahead in the 69th minute, receiving Salah's brilliant first-time through-ball before slotting past Wayne Hennessey.
Liverpool move to 86 points, 23 above Manchester City with eight matches left for their nearest rivals.
The Reds will be confirmed as Premier League champions if Pep Guardiola's side fail to win at Chelsea on Thursday.
Crystal Palace are ninth on 42 points.
Liverpool: 2 Jul v Man City (A)
Crystal Palace: 29 Jun v Burnley (H)