The victory enhances City's league position after winning just one of their five games in the run-up to Christmas
The Blues took the lead after 19mins when full-back Sam Williamson floated a free-kick into the box. Paddy McCarthy rose to head the ball down for Karl Bermingham and the striker converted from close range.
Impressive midfielder Ian Bennett sent a couple of shots wide for City but the visitors were soon level after the break, with Njazi Kuqi heading home from close range. The Finland U21 striker, brother of Shefki, had been targeted by City but joined Birmingham from FC Lahti for £385,000 last week.
He then went close on a couple more occasions but failed to find the target, while Christian Negouai was unlucky not to restore City’s lead when his shot from the edge of the box struck the inside of the post.
Ishmael Miller wrapped up the points for City though, within three minutes of replacing Negouai. Ronald Waterreus' goal-kick was headed on by Bermingham and Miller finished superbly from a tight angle to give City an 80th-minute winner.
City's next game is a visit to Nottingham Forest on 18 January.
CITY: Waterreus, Warrender, Williamson, Ireland (Etuhu 83), McCarthy, Sommeil, Bennett, Richards, Negouai (Miller 77), Bermingham, Laird (Logan 72). Subs: Schmeichel (GK), Johnson.
Birmingham: Bennett, Parratt, Davies, Blake, Taylor, Howland, Birley, Hall, Kuqi, Till, Motteram. Subs: Legzdins (GK), Hinks, Hamilton, Price, Reynolds.
Attendance: 401.