The City youngsters produced a fine all-round display at the Joie Stadium in overcoming the challenge of the German side.
A first half brace from skipper Divine Mukasa sent the Under-21s in ahead at the break.
And though Leipzig struck to reduce the deficit on 65 minutes, a third goal from Ryan McAidoo sealed victory.
It means everything is to play for going into next Tuesday’s final group game at home to Monaco with City third in the table and the top two going into the knockout stages.
“I thought it was a really entertaining game and I thought we played some really good football,” the lead coach said.
“We created a lot of opportunities and I really liked the attitude and performance.
“There was a lot to be pleased with but there are still areas where we can improve.
“It has been a really competition for us - it has tested us in different ways and if we can another good performance next week I’m sure we will be in a positive place.”
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