Jurgen Klopp’s men looked set for a shock defeat when Bobby Decordova- Reid headed the away side in front on 80 minutes, but strikes by Wataru Endo on 87 minutes and Trent Alexander-Arnold a minute later saw the result get turned on its head.
A free-kick by Alexander-Arnold which hit the crossbar and rebounded in off Bernd Leno put the hosts in front but Fulham hit back through former Red Harry Wilson.
Alexis Mac Allister’s incredible long-range effort restored the Reds’ advantage but Fulham equalised again when Kenny Tete scored in first-half stoppage time.
Decordova-Reid then appeared to have won it for Marco Silva’s men, but substitute Endo and vice-captain Alexander-Arnold had other ideas.
The result extends Liverpool’s unbeaten run in the Premier League to seven matches and two points off leaders Arsenal.
Alexander-Arnold proved to be the hero come full time and it appeared he’d got the ball rolling for Liverpool when his free-kick ended up in the back of the net on 20 minutes.
However, the goal was subsequently taken off him by the Premier League as the ball hit the bar and struck Leno before dropping into the net.
But any disappointment he felt at having that goal taken off will have been extinguished in the 88th minute as his powerful strike on the edge of the box flew into the net to give the 2019/20 champions what could be a massive three points.