Bradley Wright-Phillips missed an early chance for City but hit the opener on 31 minutes. Lee Croft's shot was saved by the Magpies keeper and Bradley knocked in the rebound.
The hosts came back, shooting wide on a number of occasions, and Nedum Onouha had to clear an Ameobi effort off the line.
But City centre-half Paddy McCarthy went close before Shaun's brother headed in Glenn Whelan's 67th minutes cross for the second.
The hosts grabbed a goal back but never threatened an equaliser. Striker Ishmael Miller almost scored after coming on before Stephen Elliott wrapped things up by converting another Whelan assist in injury time.
Manchester City: Ellegaard, Onouha, Collins, Whelan, McCarthy, Jordan, Croft, Laird (Warrender 81), Elliott, B Wright-Phillips (Miler 87), Tandy.
Subs: Timms (GK), C Logan, Etuhu.
Attendance: 317