Brian Barry-Murphy‘s side secured a place in the next stage of the European showpiece for a second successive season following a late decisive goal.
RB Leipzig took the lead from a Yannick Eduardo penalty late in the first half.
But City showed resilience and increased the intensity in the second half as they looked to secure an automatic place in the knockout stage.
Justin Oboavwoduo and Joel Ndala were constant threats out wide as City began to have a handful of half chances but nothing that could quite test goal keeper Timo Schlieck.
But it was City’s number 10, Kane Taylor, who levelled the score with a fine finish just after the hour mark.
Leipzig’s defence continued to struggle against City’s relentless attacks which included a lot of exquisite dribbling and passing sequences.
A long ball by Tomas Galvez allowed Taylor to turn provider as his pass into the box was converted by Josh Adam in the closing stages.
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