With the usual front three starting the game on the substitutes bench, it was a tough first half for the Reds as they struggled to create any clear-cut chances - entering the break without a shot on target.
Gini Wijnaldum's half-time introduction gave the Reds a slight lift as they scored the crucial opener a little under ten minutes after the restart.
But the Reds eventually sealed the game in injury time as Salah converted a penalty after being brought down in the box, with the Egyptian opening his tally in the Champions League this season.
It was an atypical performance from Jurgen Klopp's side, who appeared pedestrian in their play for much of the fixture.
Slide through our gallery below for the story of the match in photos.