The returning Diogo Jota scored a late equaliser as Premier League leaders Liverpool twice fought back with 10 men to deny Fulham following Andy Robertson's red card at Anfield.
Jota, sidelined with injury since October, slotted in an 86th-minute leveller after Rodrigo Muniz looked to have ended the Reds' second-half resistance.
Cody Gakpo's header from Mohamed Salah's sublime cross shortly after half-time had cancelled out Andreas Pereira's 11th-minute opener.
Six minutes after Pereira volleyed Fulham ahead, Liverpool's task became even tougher when Robertson was dismissed for denying Harry Wilson a goalscoring opportunity.