It was Manchester City who took the lead when defender Nathan Aké nodded in 1-0 and before half an hour was played they led 2-0.
The second goal was a huge mistake by Nordi Mukiele when his home kick went straight into his own goal.
The hill lay down on the ground saddened when he realized what he had done.
But in the 42nd minute, Leipzig reduced.
Nkunku nodded in 2-1 after a post that was beaten by Emil Forsberg.
The joy was still short-lived for the Germans when Riyad Mahrez struck a penalty just a few minutes later.
That after a hand on Lukas Klostermann.
Five goals in the second half
The second half was only a few minutes old when Nkunku came with his head again, but once again City responded quickly.
The new acquisition Jack Grealish, who made his debut in the European Cup context, got into the penalty area from the right and shot nicely in 4-2 in the far post.
A little over a quarter remained when Nkunku showed that he can also score with his feet.
After a short tussle with the defender, Yussuf Poulsen finally tucked the ball home.
Dream meeting of Cancelo
Two minutes later it narrowed once again when City's fullback Joao Cancelo got on a dream hit from a long distance.
After that, Leipzig could not get up more times.
First, the former City player Angelino was sent off after kicking down Cancelo and then Gabriel put Jesus 6-3 to the home team.
Emil Forsberg was given a chance to change things around.