Liverpool's wretched home form continued as a fine strike from Mario Lemina boosted the visitors' hope of staying in the Premier League.
The defeat ensures more misery for the Reds as qualification for next season's Champions League looks increasingly likely to arrive from winning this season's trophy.
Story of the match
As has been the case in the previous five matches, Liverpool start relatively well, making quick and incisive passes however do not have anything to show for it. The first chance arrived in the 15th minute when Xherdan Shaqiri slid the ball through right of the goal to Mohammed Salah, the Egyptian timed his run to perfection but good defending from Ola Aina and goalkeeping from Alphonse Areola prevented the Liverpool forward from scoring his 18th league goal of the season.
That is as good as it got for Jurgen Klopp's men as Fulham took control against the champions. Ademola Lookman, one of the visitors' stars of the match looked dangerous from minute one, the Englishman cut inside against Neco Williams and produced a dangerous cross to Josh Maja whose flicked effort went wide into the Kop.
Liverpool were caught out with a high line against Chelsea in midweek which resulted in a 1-0 loss courtesy of a Mason Mount goal and were nearly caught out again. Lookman driving into the penalty box, left of the goal would have made it 1-0 bar a crucial deflection from Williams sending the shot over the bar.
Liverpool huffed and puffed in the first half and went relatively close late on in the first half when a Shaqiri freekick skimmed the roof of the net from 35 yards out.
That is as good as it got in the first half for the Reds and just on the stroke of added time, Fulham got exactly what they deserved as a wonderful strike from Lemina gave the Cottagers a fully merited goal to plunge the hosts into more misery. Following a clearance from Liverpool following a Fulham freekick, the ball fell to Salah and on his heels he was easily dispossessed by the former Southampton midfielder and his strike was true into the bottom left corner past Alisson to give the Reds the same score-line at half time for the second time this week.
Similarly to the first half, Liverpool started well following the restart and nearly levelled moments after the restart when Williams cross from the right wing found the returning Diogo Jota, he proceeded to force a superb save from Areola after his stinging volley was stopped from getting the Reds back on terms.
One of the few bright moments in the second half from Liverpool was their ability to sustain attacks and win the ball high up as Fulham rarely threatened in the second half. However the sustained attacks did not warrant many efforts, bar a Sadio Mane header clipping the top of the post in the 70th minute, Klopp's men did not look like penetrating Areola's goal.
Even with the introduction of Fabinho into midfield and Trent Alexander-Arnold at right back, Liverpool didn't look any closer to ending their barren Anfield run as they endured a sixth consecutive defeat in the League.
Takeaways from the match
The Champions League should surely be Liverpool's focus to ensure Europe's premier competition is being played at Anfield next season
I think it is safe to say, and most Liverpool fans would agree that a place in the top four looks all but over even with ten games to go. Whilst Jurgen Klopp may look optimistic in front of the cameras even he will surely believe that winning the European cup will prove to be a more viable option.
Thankfully for his side they don't have to win their game against RB Leipzig in the Puskas Arena on Wednesday night as a 2-0 win in the first leg has put Klopp's side in control and a goalless draw away from reaching the last 8.
Fulham's superb form continues as they pile the pressure on Newcastle and Brighton
The race to avoid the drop looks increasingly exciting for football fans as results this weekend have made the relegation battle even tighter. Fulham's victory coupled with a defeat for Brighton against Leicester City and Newcastle United's draw against West Bromwich Albion have made the bottom of the table extremely congested as those three clubs are separated by one point.
Scott Parker should take immense pride in how he has turned his side's from around, following the start of the season many bookmakers predicted the Cottagers to be the first to go down however since then he has drilled the team to perfection as it looks likely that they will be playing in the Premier League again next season.