Birmingham edged a keenly-contested Midlands derby to give Chris Hughton his first points as Blues manager.
Hughton was instrumental in the outcome of the match as the introduction of sub Adam Rooney proved a turning point.
Rooney first headed against the post before reacting quickest to tee-up the rebound for Keith Fahey to smash home the 73rd-minute winner from 10 yards.
Coventry had their chances with Lukas Jutkiewicz wasting their best chance in the first half when he shot wide.
Birmingham improved after the interval and Chris Wood blazed carelessly wide after being set-up by Jean Beausejour.
Once ahead, the home side slowed the match down and made certain of three points.