It took a 31st attempt for the Cottagers to finally salute at the Merseyside venue with the collection of three points allowing them to go equal with the eighth-placed Reds who have won just one of their past eight at home.
Kenny Dalglish fielded a much-changed line-up from the team that beat Norwich City on the weekend, preferring to rest the likes of Luis Suarez, Steven Gerrard, Pepe Reina, Daniel Agger, Glen Johnson and Jose Enrique, as he prepares his players for this weekend's FA Cup final against Chelsea.
It was a great chance for Fulham, without ill manager Martin Jol, to end their barren run at Anfield and the deciding goal came in quite fortuitous circumstances in just the fifth minute.p>Clint Dempsey made a very clever run before knocking it into the path of ex-Reds full-back John Arne Riise who hammered it towards Alex Kacaniklic whose touch deflected onto Martin Skrtel and in past Doni for an own goal which was the West London clubs first at the venue since March 2006.
Fulham were providing the better of the chances early with Pavel Pogrebnyak forcing a close range save from Doni when he got his outstretched foot to Dempsey's chipped through ball in the 15th minute.
Liverpool weren't without their chances either with Brede Hangeland producing a timely goal-line clearance to deny Jonjo Shelvey in the 28th minute after Fulham keeper Mark Schwarzer had spilled an Andy Carroll-bound cross before the Australian saw Shelvey's attempt trickle past him but fortunately the Norwegian centre-back was perfectly placed.
Just before the break, Carroll saw his powerful header directed straight at Schwarzer prior to another huge play from Hangeland who cut down Maxi Rodriguez after he has bust past Aaron Hughes on the left before foraying into the area.
Cottagers substitute Kerim Frei almost made an immediate impact when his 62nd minute attempt from just outside the area beat Doni but not the Brazilian's front post moments before the Reds gloveman denied former Roma teammate Riise who had advanced down the left.
Doni then came up with another massive save to keep out Dempsey who had been slipped through by the ever-impressive Frei before Skrtel almost capped off an average night by producing a horror headed backpass which thankfully Doni was on hand to thwart Dempsey's flicked effort.
In the end, however, it was a deserved win for Fulham who erased the sour memories of the weekend's 4-0 loss across the park at Everton with assistant Billy McKinlay doing the job whilst Jol was resting at home with a chest infection.
Anfield, Liverpool - 40,106
Yellow cards:LIV - nil FUL - nil