Liverpool made it three wins from three in the Champions League as they continued their surprisingly excellent start to the season.
Arne Slot has won all six of his away games in all competitions as Liverpool boss and 11 wins from our opening 12 games is a club record.
And it was another narrow win, with a clean sheet - although this one was a little more fortuitous.
Jurgen Klopp takes up his position as head of global soccer at Red Bull in January and it was perhaps fitting that the often misaligned Darwin Nunez proved to be the matchwinner - although his touch perhaps didn't alter the outcome from Mo Salah's attempt which was heading in anyway.
Leipzig started the brighter - had a couple of chances and a weak header from Kelleher, miles out of goal, almost gave the reds an early scare against a team that have started very well in the Bundesliga this season.
Tsimikas sent in a cross that Salah headed towards goal - Nunez tapping it in relegating Salah's header to an assist.
1-0.
Nunez could have had another but for a fine tip over the bar from former LFC keeper Peter Gulacsi.
Nunez should have had a penalty when he was fouled by Orban. A strange decision not to give the spot kick even after reviewing it on VAR.
Leipzig had a couple of disallowed goals for offside, but it was Liverpool who did deserve the win and alongside Aston Villa are the only two teams of the 36-team competition to have a perfect record.
Slot was thrilled with the work-rate, but less thrilled that the reds hadn't been clinical enough to end the game by the 70th minute.
The reds travel to Arsenal on Sunday for what will be the most serious examination to date.
MOTM: Virgil van Dijk
Watch the match highlights from Leipzig 0-1 Liverpool