The Sky Blues made it three games unbeaten in the Championship after Max Biamou struck late at Carrow Road.
City had fallen behind midway through the first half to a controversial penalty, which Mario Vrancic ultimately slotted past Ben Wilson.
However, the Sky Blues controlled the game from then on and waited patiently to grab an equaliser, which came in the 89th minute, when a lovely ball played out wide to Ryan Giles by Gustavo Hamer was met first time by the wing-back and he spotted Biamou and Walker in the box, with the ball eventually breaking to Max, who slotted the ball home.