Martin Skrtel, Steven Gerrard and Stewart Downing provided plenty of festive cheer for the red half of Merseyside, with Brendan Rodgers' side moving up to eighth place in the Premier League standings.
Fulham, meanwhile, have now won just once in their last 10 and need to find inspiration from somewhere if they are to avoid entering 2013 looking anxiously over their shoulder.
Unlike last weekend, when Liverpool dominated the opening half-hour of their encounter with Aston Villa but failed to score and paid the price, they got the break they needed early on.
Gerrard's eighth-minute corner picked out Skrtel, who had barely moved, and with former Reds full-back John Arne Riise slow to close down the Slovakia international he brought the ball down and smashed a volley past Mark Schwarzer.
Daniel Agger's miss from just three yards - blazing into the top tier of the Anfield Road stand from Suarez's cross - may have resurrected fears about not being clinical enough in front of goal. But those insecurities were put to bed in the 36th minute with Downing's first significant intervention.
The England international's brilliantly-disguised reverse pass from the edge of the penalty area deceived everyone except Gerrard.
Liverpool's captain seized on the flat-footedness of Fulham's defenders to clip a shot across Schwarzer and just inside the far post.
Suso scuffed a shot wide and Suarez fired straight at the goalkeeper before the interval but within six minutes of the second half the result was put beyond any doubt.
Gerrard, who had one of his better days spraying passes all over the field, picked out Downing on the right wing and he cut inside before blasting home a shot which appeared to release months of pent-up frustration.
The 28-year-old played like a man with a point to prove at times and saw another blistering drive sail just over the angle of crossbar and post.
Schwarzer did well to block Gerrard's close-range shot as Liverpool continued to press, Jose Reina did less well with Dimitar Berbatov's long-range effort which squirmed from his grasp and required Skrtel to clear.
But that was a rare moment of concern on what was a trouble-free evening as Liverpool recorded only their fourth home league win of the season when Suarez side-footed home in added time for his 11th league goal of the season - equalling his tally from the whole of last season.
| Liverpool | Team Statistics | Fulham |
| 4 | Goals | 0 |
| 2 | 1st Half Goals | 0 |
| 9 | Shots on Target | 4 |
| 9 | Shots off Target | 2 |
| 5 | Blocked Shots | 2 |
| 8 | Corners | 2 |
| 13 | Fouls | 6 |
| 2 | Offsides | 0 |
| 1 | Yellow Cards | 2 |
| 0 | Red Cards | 0 |
| 87.3 | Passing Success | 83.5 |
| 24 | Tackles | 18 |
| 87.5 | Tackles Success | 83.3 |
| 55.6 | Possession | 44.4 |
| 51.7 | Territorial Advantage | 48.3 |
| 553 | Total Passes | 431 |
| 22 | Total Crosses | 10 |
| 125 | Lost Balls | 131 |
| 61 | Recoveries | 58 |
| 61.7 | 1st Half Poss. | 38.3 |
| 50.6 | 2nd Half Poss. | 49.4 |
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