The Reds looked set to drop key points in the Premier League title race, but as has so often been the case in the past, late drama ensued.
Bernd Lenos own goal after Trent Alexander-Arnolds free-kick hit the crossbar opened the scoring, while Alexis Mac Allister and Wataru Endo scored with spectacular efforts.
It was then left to Alexander-Arnold to win it with time running out, burying a finish in front of the Kop to put Liverpool within two points of league leaders Arsenal.
Here we compare our player ratings with those of the Liverpool Echo, Goal, FotMob and This Is Anfields readers.
Alexander-Arnold (8.5) was Liverpools star man by a country mile at Anfield, as he continues to produce brilliance for his boyhood club.
The 25-year-olds free-kick was actually given as a Leno own goal, which seems cruel, but there was no doubt about his inch-perfect winning strike.
Aside from his goals, the Echos Ian Doyle thought that Alexander-Arnolds passing regularly poked holes in Fulham rearguard, also hailing his superbly-struck free-kick.
Peter McVitie of Goal did claim that he should have been tighter to Harry Wilson to block the goal, but TIAs Henry Jackson gave him the Man of the Match award.
In second place behind Alexander-Arnold was Mac Allister (7.6), no doubt helped by his incredible strike to put Liverpool 2-1 up.
It was a stunning first Reds goal for the Argentine, but FotMob also pointed out that he completed 85 percent of his passes joint fourth-best of any Red and made six recoveries.
Next up in the ratings was Virgil van Dijk (6.8), with the captain not necessarily at his very best, but still solid overall.
Dolye felt that his diagonals caused Fulham issues early on, and Jackson described Liverpools towering centre-back as strong in his all-round game.
The worst rating went to Caoimhin Kelleher (4.2), with the Irishman not great for two goals and looking a far cry from the level of the absent Alisson.