The Reds thought they went in front inside eight minutes through Mohamed Salah, but the goal was ruled out for an offside in the build-up.
Nonetheless, Liverpool did eventually find the breakthrough as Trent Alexander-Arnold’s superb free-kick cannoned in off Bernd Leno’s back after hitting the underside of the crossbar.
None of the last 11 H2Hs at Anfield had seen both sides score, but Fulham broke that run with their first shot on target in the game, as ex-Liverpool youngster Harry Wilson tapped in Antonee Robinson’s cross.
The hosts needed inspiration, and they got it in abundance from Alexis Mac Allister, who will remember his first Liverpool goal for the rest of his life - an absolute screamer into the top corner from long distance.
Still, there was time for the visitors to strike again through Kenny Tete, as he poked home Raúl Jiménez’s flick-on from a corner in added time, as Jürgen Klopp’s team looked particularly vulnerable from set pieces.
Remarkably, Fulham scored from their next corner minutes later through Tim Ream, however, his close-range effort was ruled out by the offside flag - bringing an end to a tumultuous opening period.
Liverpool came out in the second half determined to extend their unbelievable winning record at Anfield, where they had won all but one of their last 48 PL games, and Darwin Núñez - who had a 100% record in PL home matches he had scored in - was the width of the crossbar away from giving them the lead inside the first 10 minutes.
Salah was the provider, as he has often been this campaign with five assists before today, and the Egyptian set up another glorious chance for Núñez on the hour-mark, but the striker skewed wide from a promising position.
Fulham did not give up though, and with 10 minutes to go, the shock comeback was complete.
Two substitutes combined in Tom Cairney and Bobby Decordova-Reid, and it was the latter who headed in at the far post after some brilliant work from Robinson, who still had the energy to bomb forward from left-back.
This match was chaotic from the start, and it did not stop until the end, as two late goals turned Liverpool’s fortunes around.
Wataru Endo curled in his first PL goal for the club in what was a fabulous finish from outside the area, before Alexander-Arnold completed a dramatic comeback by unleashing an unstoppable strike into the corner.
The result ensures the Reds keep up the pace with league leaders Arsenal at the top, with Manchester City to play Tottenham Hotspur in the late kick-off, while Marco Silva will be absolutely gutted with what unfolded, as Fulham still search for their first away league win this term, and stay in 14th place in the table.
Flashscore Man of the Match: Trent Alexander-Arnold (Liverpool)
