Jurgen Klopp’s team may have written off their chances of winning back-to-back Premier League titles after losing three successive domestic matches but they gained a clear advantage in their European tie going into the March 10 return leg.
Salah easily intercepted a back pass by Leipzig’s Marcel Sabitzer to put the visitors ahead in the 53rd minute and on course for their first win in any competition since late January.
Mane then pounced on another mistake when Nordi Mukiele failed to clear a long ball five minutes later, leaving the Germans down for the count in Budapest’s Puskas Arena where the game had been relocated due to COVID-19 restrictions in Germany.
The Germans got off to a better start and Dani Olmo’s downward header in the fifth minute bounced off the base of the post.
With Leipzig defending high, Liverpool initially tried to slice through with deep crosses and one of them found Salah in the 15th but his chip was blocked by keeper Peter Gulasci.
Andy Robertson then tried his luck with an audacious 40-metre lob that almost caught Gulasci out of position but they had to wait until the 53rd to strike with their first chance of the second half.
Leipzig coach Julian Nagelsmann then saw his players gift away another goal with Mukiele’s error and Mane’s crisp finish.
Leipzig, who came into the game on a four-game winning run in all competitions, were largely toothless in attack following the two goals until Tyler Adam’s miss in stoppage time.