Both goals came in a two-minute spell during the first half with Emil Forsberg putting the Bundesliga side ahead and Youri Tielemans immediately replying for last season's semi-finalists in the Group G game.
It was the first time a team from Leipzig had played a European club competition game since Lokomotiv Leipzig, now in the fourth tier, hosted Diego Maradona's Napoli in 1988 in what was then East Germany.
Leipzig were only officially founded in 2009 after buying the licence of fifth-tier SVV Markranstadt and quickly rose through the ranks with the financial backing of the Red Bull energy drinks company, finishing second on their Bundesliga debut last season.
Forsberg scored their first European goal when he was set free down the left and sprinted 30 metres before planting the ball past Diego Benaglio.
They barely had time to celebrate before Fabinho's cross from the right was headed back across goal by Adama Diakhaby to Tielemens whose first effort was well-saved by Peter Gulacsi but the Belgian forward snapped up the rebound.
(Writing by Brian Homewood; Editing by Clare Fallon)
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