Liverpool's Mohamed Salah celebrates scoring the 1-0 goal during the UEFA Champions League semi final, first leg soccer match between Liverpool FC and AS Roma at Anfield, Liverpool, Britain, 24 April 2018. EPA-EFE/PETER POWELL 
Juergen Klopp's side were outplayed by Scott Parker's adventurous team before halftime at Craven Cottage and trailed to Bobby Decordova-Reid's superb 25th-minute effort.
They were more like themselves after the break and levelled in the 79th when Salah beat Alphonse Areola from the spot after a rather harsh handball decision.
The visitors looked likely to go and grab the winner but Fulham held out for a well-deserved point to leave Liverpool level on 25 points with leaders Tottenham Hotspur.
Fulham are fourth from bottom with eight points. (Reporting by Martyn Herman Editing by Toby Davis)