Jurgen Klopp's side welcomed the Cottagers to their Merseyside back on the back of 10 successive wins from 10 home games in the 2023-24 season, including a 4-0 Europa League thrashing of LASK Linz on Thursday.
After unsurprisingly putting out a rejigged XI for that continental affair, Klopp reverted to a full-strength side for the visit of Fulham, who travelled north on the back of a thrilling 3-2 beating of Wolverhampton Wanderers on Monday.
It came as no surprise to see Liverpool start the brighter at Anfield, and they were rewarded when a Trent Alexander-Arnold free kick struck the back of Bernd Leno and bounced over the line.
However, Klopp's men were sloppy defensively and allowed Fulham a route back into the game through former winger Harry Wilson, who poked home through Caoimhin Kelleher's legs after being teed up by Antonee Robinson.
A 30-yard Alexis Mac Allister thunderbolt restored the hosts' one-goal advantage, only for Kenny Tete to capitalise on more lackadaisical Reds defending just before the break to draw Fulham level again.
After Darwin Nunez squandered a couple of chances to bag Liverpool's third, Klopp's men were staring down the barrel of defeat when Bobby Decordova-Reid outmuscled Kostas Tsimikas and headed home at the back post in the 80th minute.
The Cottagers' lead lasted all of five minutes, though, as Wataru Endo curled home a stunning leveller in the 85th minute, two moments before an Alexander-Arnold drive completed a remarkable Liverpool fightback.
With Fulham's third goal of the afternoon coming in the 80th minute, Liverpool set a new club record on Sunday,
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