Rodgers made a range of changes including a switch to four at the back in came Agger, Johnson and Coutinho while Enrique returned on the bench, Liverpool started well with Agger hitting over after latching on Skrtel's pass while Coutinho shot wide.
Coutinho picked out Gerrard who in turn found Suarez and he attempted to set up his strike partner Sturridge but was denied by Stekelenburg, Fulham countered through Berbatov as he swept over a cross to Kasami but the resulting shot was blocked.
Mignolet soon denied Berbatov who clipped a chance towards goal but it was in vain minutes later as
Liverpool opened the scoring, Gerrard swept in a free kick which was flicked on by Agger and Suarez but went in off Amorebieta to Fulham's embarassment.
The vistors' mood got worse within minutes as Liverpool converted from another set-piece after Gerrard hit a superb corner which met the head of Skrtel who celebrated his first goal in 11 months since scoring against Fulham last December.
Liverpool pushed on for more and Coutinho hit a brilliant volley which was destined for the top corner only for Steklenburg to deny him a comeback goal and he was denied for a second time when his drilled shot was saved by the 'keeper.
Suarez got his name on the scoreboard with 36 minutes played as he connected to a through pass by Henderson and finished with style past his former Ajax teammate to pile the pressure on former boss Martin Jol and give Gerrard praise for a sweet nutmegging of Berbatov which had set the play up for Henderson.
Liverpool looked to continue where they left off as the SAS combined only to be denied by Stekelenburg including a rebound which missed the target but the wait for a fourth goal only took until the 54th minute when Gerrard played in Suarez who hit his eighth league goal of what has been a short season for him and he could have hit a quick third with a lob from halfway but it failed to trouble the 'keeper.
Fulham had a great chance to pull one back via Kasami's long-range effort but Liverpool continued their assault with Allen and Moses in place of Gerrard and Sturridge and there was a late appeal for a penalty for a tackle on Henderson but Parker's challenge was impressive and the right call was made.
Liverpool held on for a first clean sheet in eight games and sit second in the table going into the international break.