Liverpool were handed a fortunate break in the final ten minutes as Fulham goalkeeper Sergio Rico impeded Sadio Mane in the danger area to give the Reds a penalty.
Substitute James Milner stepped up to confidently convert for the Reds and rescue a valuable three points.
It caps off a perfect week for the Reds, having defeated Bayern Munich in the Champions League on Wednesday night to progress to the quarter-finals.
They now sit in first place in the Premier League over the March international break, two points above Manchester City who have a game in hand.
Slide through our gallery below for all the best photos from a nervy afternoon at Craven Cottage.