A Kolo Toure own goal had spotted the hosts the early lead, but Daniel Sturridge had the guests back on level terms before the interval.
Then it was Kieran Richardson’s turn to restore Fulham’s advantage, although just minutes later Philippe Coutinho’s shot had taken a deflection off Willian Kvist and found its way past Cottagers goalkeeper Maarten Stekelenburg.
Following are player ratings and analysis for all the Liverpool players.
Mignolet: Had no chance on the Toure own goal and had only one other save to make.
Flanagan: Winning his battle against John Arne Riise.
Skrtel: Has completed 94 percent of his passes so far.
Toure: Capped an abysmal first half, during which he also clattered into referee Phil Dowd, with an own goal.
Cissokho: Much of what Liverpool are doing is coming from the right—he has so far had only 26 touches.
Coutinho: Imposed himself more and more as the first half went on.
Gerrard: Delivered one of the best through balls you’re likely to see in the buildup to the Sturridge equaliser.
Henderson: Exceptional distribution of the ball so far.
Sterling: Finding Dan Burn a difficult centre-back to cut in on.
Suarez: Dropping deep to better involve himself.
Sturridge: Took his goal—a deft, left-footed effort that hit the inside of the far post before crossing the line—exceptionally well.
Mignolet: Made two saves on the night and was beaten by his own defense on the pair of Fulham goals.
Flanagan: Carving a place for himself as manager Brendan Rodgers’ first-choice right-back.
Skrtel: Got tangled up with Flanagan ahead of the Richardson goal.
Toure: Made a vital tackle on Bent to make amends for his own goal.
Cissokho: Distribution from the left was excellent, even if the Reds tended to operate down the right.
Coutinho: Left a trio of white shirts in his wake as he cut inside before hitting a shot that deflected off Kvist on its way to goal.
Gerrard: Picked up a goal and an assist in a superb, all-around performance.
Henderson: His superb movement always provided Coutinho and Gerrard with a passing outlet.
Sterling: A useful, if not subdued showing, and he was replaced by the youngster Teixeira in the 82nd minute.
Suarez: His work-rate was through the roof in the second half, even if it didn’t pay off in a goal.
Sturridge: Delivered a short, delicate pass to Coutinho to set up the equaliser.
Teixeira: Flashed an audacious effort over the crossbar shortly after taking his Premier League bow.
Agger: Was brought on to shore things up in the final moments.
Statistics courtesy of Who Scored?