Bobby Decordova-Reid gave the advantage to the home side with 25 minutes gone by way of an emphatic effort from the edge of the area.
Alisson Becker made a glorious return and propped up an otherwise struggling Liverpool team in the opening period with some vital stops.
Liverpool's blushes were spared as Salah's tame penalty snuck under Alphonse Areola, after a dubious call for handball on Aboubakar Kamara.
Evaluating the result
'...but then half-time helped massively and the second half was much better. I think in the first half an hour we could have lost the game, in the last 60 minutes we should have won it. In the end we get a point and that’s it.'
It was astonishing that Jurgen Klopp had a voice to talk to the media with after his team's performance in the first half-hour instigated his audible barking from the touchline.
An extremely laboured opening period from the Reds afforded Fulham a lot of time on the ball and invited pressure.
The Cottagers had several chances consequentially that could have put them deservedly in front and by a fair margin but for Alisson's solid goalkeeping.
It was nonetheless a much-improved attitude to the game in the second half after what was an uncoordinated approach, turning the tables by making Fulham sit in their own half for large portions of the game's remainder.
The return of Alisson
“You could see in one or two situations you could see that he needs rhythm too, but in the key moments he was there. Sensational saves, obviously, but the goalkeeper on the other side had a pretty important job to do as well.”
The Brazilian number one has sat out the last three games with a hamstring injury, but the consequences were mitigated by a series of tremendous performances from young Irish goalkeeper Caoimhin Kelleher.
Alisson continued the solid recent performances between the sticks at Craven Cottage with numerous memorable saves.
Ivan Cavaleiro had a trio of great opportunities throughout the game and was denied on all three occasions, the first of which was a blistering hit that Alisson did well to parry away.
A low curled shot from Ademola Lookman put Alisson to the test again in the first half but the former typically prevailed in what was a triumphant return to the lineup.
VAR and a possible foul
'It's a clear foul, nothing else. It's not a yellow card offence, its not a red card offence, nothing else.'
Antonee Robinson was able to lay off the ball to Decrdova-Reid before the Jamaican excellently put away his chance to open the scoring.
Jurgen Klopp, however, believed the way in which Robinson retrieved the ball from a breaking Mo Salah was in fact illegal.
Lee Mason deemed the contact made as 'normal' and decided there was no clear and obvious error in Andre Marriner's judgement, allowing Fulham's goal to stand.
Liverpool were involved in more VAR drama when Fabinho seemed to have brought down Cavaleiro in the box while making contact with the ball, prompting Marriner to look for himself at the video monitor but stuck by his initial judgement.
Joel Matip injury
'Matip has a spasm in his back, but we will see. At the moment, nothing else. He already got treatment and will be getting treatment so I think there is a chance for Wednesday.'
It looked to be more troubling times for Liverpool and their physio bench after Joel Matip left the field with a back spasm.
The devastating news that Diogo Jota will not be available for the next two months with a knee injury was compounded by the possible absence of one of the Reds only fit senior centre-backs ahead of the top-of-the-table clash against Spurs on Wednesday.
The uncertainty surrounding Matip will not boost confidence with the likes of Heung-Min Son and Harry Kane visiting Anfield on Wednesday having added to their tally of 12 assists for each other when fumbling their lead to Crystal Palace this afternoon.
Selection for Tottenham
'We are not struggling with numbers in the centre-back positions. We have some, they are just getting younger and younger – [but] we still have centre-backs. Today we brought Hendo into that position.'
Jordan Henderson was made available to shift position in wake of the Cameroonian's departure after initially starting at the base of the midfield three.
It is unlikely such a situation will occur again. With the possibility of Matip on the sidelines, it is likely youngsters Rhys Williams and Nat Phillips could be in with a shout to deputise.
Williams (19) and Phillips (23) have played a much larger role than expected with injuries to Matip and of course Virgil van Dijk and Joe Gomez, making five appearances between the pair in all competitions this season.