The England international's late double completed a dramatic comeback for Manuel Pellegrini's men, who came from 2-1 down to defeat the Bundesliga outfit and finish top of Group D
Manchester City will go through to the round of 16 as the group winner after a come-from-behind 4-2 victory over Borussia Monchengladbach.
David Silva opened the scoring early on, smashing his finish into the top corner of the net after being played through by Raheem Sterling.
City's lead did not last long, however, Julian Korb stealing in at the far post to turn home Lars Stindl's cut back just three minutes later.