The game began at a high tempo, with both teams showing plenty of attacking intent.
Leipzig started brightly and had an early chance in the second minute when Amadou Haidara won the ball high up the pitch and squared it for Xavi Simons.
However, the Dutch international’s first-time effort flew over the bar.
Moments later, Leipzig came close again through Benjamin Sesko, whose header was comfortably saved by Kelleher.
Despite Leipzig’s early pressure, it was Liverpool who struck first in the 27th minute.
Salah, who had been a constant threat on the right flank, provided the assist.
After a neat exchange of passes, Salah’s header across goal found Nunez in the right place at the right time, allowing the Uruguayan striker to tap home from close range.
Leipzig thought they had equalized just minutes later when Lois Openda found the back of the net with a powerful strike.
However, the Belgian forward was ruled offside, much to the relief of the Liverpool defence.
As the game progressed, Leipzig had more opportunities to draw level, with Openda again causing problems for the Liverpool backline.
In the 73rd minute, Kelleher made an outstanding save to deny Openda after a brilliant solo run by Simons.
The Liverpool goalkeeper, who was in fine form throughout the match, made several key saves to preserve his team’s lead, including another crucial stop in the 77th minute to deny a long-range effort from Sesko.
Liverpool, meanwhile, looked dangerous on the counter-attack, with Cody Gakpo and Luis Diaz creating chances to double their lead.
In the 70th minute, Alexis Mac Allister came agonisingly close to scoring when his curling shot from 20 yards out rattled the crossbar.
Gakpo also had a chance to seal the victory late on but was denied by Leipzig goalkeeper Peter Gulacsi, who managed to parry the Dutchman’s goal-bound effort.
As the clock ticked down, Leipzig pushed for an equaliser, and their best chance came in stoppage time.
Christoph Baumgartner threaded a pass through to Openda, who found himself in a promising position.
Instead of taking the shot himself, Openda opted to square the ball to Yussuf Poulsen, but his misplaced pass allowed Liverpool to clear the danger and take the points.
