It was to be another afternoon to forget for beleaguered Cottagers boss Martin Jol, with little resistance offered during a third straight defeat - and a seventh in total this season.
The visitors to Anfield never got out of the blocks, with the returning Daniel Agger and Philippe Coutinho going close in the opening exchanges.
The warning shots had been fired at Fulham, but they were not heeded and Liverpool broke the deadlock on 23 minutes when Luis Suarez touched on a Steven Gerrard free-kick and the ball nestled into the bottom corner off the unfortunate Fernando Amorebieta.
Fulham's Venezuelan defender was to endure a rough few minutes, as he then allowed Martin Skrtel to run off him moments later and nod home another pinpoint Gerrard delivery - this time from a corner.
Buoyant Liverpool ended the game as a contest on 36 minutes, with Jordan Henderson threading a perfect pass into the path of Suarez to drill low under Maarten Stekelenburg.
Nine minutes into the second half and the Uruguayan netted his eighth goal in just six top-flight outings this term, making no mistake in a one-on-one situation after Gerrard had caught Kieran Richardson napping and sent the in-form frontman racing clear.
Jol has resolutely insisted in recent weeks there are a number of teams worse than his in the Premier League but a look at the table, with the Cottagers hovering dangerously above the relegation zone in 16th, suggests otherwise.
They arrived with containment in mind, fielding Dimitar Berbatov as a lone striker, and for 20 minutes they managed just that, albeit not too convincingly.
They even managed a half-chance, with Pajtim Kasami's shot deflected into the side-netting after Berbatov's 50-yard cross-field ball had released Elsad Zverotic to cross from the right.
It took a set-piece to break Fulham's fragile resistance but once the defence had been breached it was open season on the Cottagers' goal.
Gerrard whipped in a near-post free-kick which Suarez and Agger, starting his first match since 24th September as Liverpool reverted to an orthodox back four, both challenged for with the former appearing to get the touch which diverted the ball on to Amorebieta and inside the post.
Having conceded three times in 12 minutes against Manchester United a week ago, the last thing Fulham needed was to let in another quickly. So to be undone at another set-piece would have infuriated Jol.
Again Gerrard's delivery was perfect, the corner sent over with just the right amount of pace to allow Skrtel to power home a header - his first goal since 22nd December 2012, which also came against Fulham.
Liverpool's third was the culmination of a 36th-minute move which saw Gerrard out-Berbatov Berbatov, the king of the fancy flick, with a brilliant reverse nutmeg close to the halfway line before the England captain sprayed a pass out to Jordan Henderson on the right.
The newly-recalled England international slid an inch-perfect ball down the channel for Suarez to fire home first time.
After the break there was no let-up and, had it not been for goalkeeper Stekelenburg, the only Fulham player to emerge with any credit, who knows what the final score would have been.
The Dutchman, who had already produced a great save to tip over a rising Coutinho drive in the first half with the score at 2-0, blocked shots from Suarez and Sturridge in the same attack before Suarez volleyed the rebound from the second strike over an empty goal.
But the Uruguayan was not to be denied and when Gerrard robbed Richardson and threaded a pass forward, Suarez dropped a shoulder to move Philippe Senderos slightly off balance before drilling home inside the near post.