Lucas' suspension meant he was replaced by Sterling in an otherwise unchanged Liverpool side who started the better with Suarez finding space to setup Gerrard who hit a swooping shot which was denied a chance at goal by Delaney.
Palace responded when Puncheon picked out Jerome only for the striker to head wide of the goal, but the deadlock could have broken in the 11th minute as an unmarked Moses attempted a flick which didn't come off as he had hoped.
Liverpool opened the scoring in style as Suarez linked up with Enrique to sway through the Palace defence and drive the ball past Speroni for his third goal in two games and the lead was increased to two within four minutes as Sturridge shimmied past the challenging defenders to hit into the far corner and send the home fans into celebration.
Palace needed a quick response and were unlucky not to comeback to 2-2 as Kebe raced passed the home defence and hit goalwards beating Mignolet but denied by Toure's clearance off the line and the rebound from Kebe was saved by Mignolet. Jerome swept in a cross which deflected off Toure but luckily for Liverpool was cleared by Sakho.
Their failure to convert from previous chances cost Palace as their hopes of a comeback were dealt a big blow as they conceded a penalty in the 37th minute after Sterling was tripped and Gerrard converted past Speroni for a 3-0 lead.
Three could have become four as Moses after connecting to a Suarez pass hit the crossbar while Suarez himself tested Speroni with a drive to the left but was denied as the Reds went in 3-0 up at the break.
The second half was devoid of any real action until a chance from Sterling tested Speroni, Puncheon was denied by Mignolet after his shot deflected off a Liverpool defender and Gayle swept a powerful strike over the bar.
Agger came on for Sakho as Palace threatened to damaged Liverpool's clean sheet and were soon successful as after Sterling was penalised for a foul,Campana swept in a dangerous free-kick which Gayle latched onto to glance the ball into the corner past Mignolet and give Palace hope at 3-1.
It was consolation if anything for Palace who could have gone three behind again as Sturridge hit a shot from the edge of the box which struck the post but Liverpool claimed a 3-1 win which sent them top of the league until this afternoon when Arsenal's draw put them top on goals scored but to be joint top into the international break is great considering where we were a year ago.