Hoolahan took advantage of an error by veteran midfielder Graham Kavanagh to slot the ball home from eight yards and end the Cumbrians' own four-game unbeaten run.
Defender Ian Harte and winger Matty Robson were both denied at close quarters as Carlisle tried to break down a solid Norwich rearguard in the first half.
But the Canaries were playing good possession football and Carlisle-born skipper Grant Holt was only kept out by a valiant last-ditch challenge from Tom Taiwo.
A badly judged back header by Harte nearly let in Adam Drury, and it was a series of errors that enabled the visitors to grab the lead just before half-time.
Chris Martin's cross from the left eluded both Harte and Richard Keogh, and when Kavanagh slipped in attempting to clear, Hoolahan pounced on the loose ball to slide a shot home from eight yards.