Trent Alexander Arnold celebrates
Trailing 3-2 in the 87th minute, Liverpool equalised as Wataru Endo scored his first Premier League goal and seconds later Alexander-Arnold completed the turnaround.
Alexander-Arnold had helped Liverpool open the scoring in the 20th minute when his free-kick ricocheted off the crossbar and in off Fulham keeper Bernd Leno.
Former Red Harry Wilson equalised four minutes later before Alexis Mac Allister restored Liverpool's lead after 38 minutes with a stunning long-range strike.
Kenny Tete netted Fulham's second equaliser in first-half injury time and Bobby De Cordova-Reid headed the Cottagers into the lead in the 80th minute.
Fulham had looked set to end Liverpool's 13-month unbeaten home record in the Premier League. Instead, the Reds kept up their perfect record at Anfield this season and cut Arsenal's lead at the top to two points.
Marco Silva's side stayed 14th.
-- Courtesy of BBC Sport