Robinho's place was taken by Daniel Sturridge, who provided the cross that Benjani Mwaruwari slotted into an open goal at the far post in the 32nd minute.
Having had a goal ruled out for offside, Stephen Ireland slotted the ball under the advancing Schalke goalkeeper Manuel Neuer in the 66th.
City's next opponent, Paris St. Germain, was held 2-2 by Racing Santander after squandering a two-goal lead and stay bottom of Group A.
In Group F, Leonardo pushed four-time European champion AJAX up to second with a 1-0 win at Hamburg, and MSK Zilina and Slavia Prague won their first points by drawing 0-0.
Luciano Galletti scored in the first minute and set up two goals as Olympiakos routed Benfica 5-1 in Group B, where leader Galatasaray lost 1-0 at home to Metalist Kharkiv. In Group G, 2004 champion Valencia routed Rosenborg 4-0 to claim its first win, while French league strugglers St. Etienne progressed despite Brugge's Ronald Vargas cancelling out David Gigliotti's opener.
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