Norwich striker Grant Holt thought he had given his side a 13th-minute lead, but his header was cleared off the line by Joleon Lescott.
Lescott's clearance proved to be even more important in the 18th minute when Carlos Tevez broke the deadlock. The Argentine collected possession from Silva before swerving a shot past Ruddy from a narrow angle.
City doubled their advantage after 27 minutes when Tevez linked with his fellow countryman Sergio Aguero, who fired into the top corner from 18 yards out.
Holt had a chance to reduce the deficit as the half drew to a close, but his low shot from a Russell Martin cross was held by Hart.
City's rivals United take on Aston Villa tomorrow afternoon.