Kyle Walker‘s first-half goal against his former club was enough to secure the three points for Pep Guardiola’s side.
City climb up to seventh in the table while Chris Wilder’s side continue their winless run and remain in the bottom three.
The visitors went ahead after 28 minutes when Walker unleashed low drive into the bottom corner.
Kevin De Bruyne almost doubled City’s lead 10 minutes after the break but his shot went just wide.
With 20 minutes to go, John Lundstram missed United’s best chance to equalise after his close range shot went over the bar.
The hosts failed to register a single shot on target throughout the 90 minutes.