However, Bernardo Silva, who made his 22nd appearance across all competitions this season against Marcelo Bielsa's men, was replaced by Ilkay Gundogan at the interval, which caused concern over the Portugal star's fitness.
Leipzig had to wait till the 85th minute to break the deadlock.
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Gundogan was desperately unlucky not to score with two decent chances, and his wastefulness was nearly punished.
The 24-year-old has scored three goals in 12 Premier League appearances for City this season and his form has been integral to Pep Guardiola's side's recent success.
The former Barcelona teen showed some nifty footwork to tee up Bernardo to score his second of the game with a crisp strike.