The Tigers took the lead against the run of play in the 83rd minute when Robert Koren headed home after Andy Dawson's shot had deflected off Elliott Ward and Tom Cairney's stunning 20-yard free-kick wrapped up the points with two minutes left.
It was the first time the Tigers had tasted success on the road since beating Fulham 1-0 at Craven Cottage in March 2009 - a run of 30 games - while Norwich slipped to their second loss in three games.
Norwich were unchanged from their 1-0 win at Preston although there was a place on the bench for Steve Smith, who was in the matchday squad for the first time since his summer switch from Rangers having recovered from an ankle injury.
Captain Ian Ashbee returned to the Hull line-up in place of John Bostock to make his 250th appearance for the club. Jimmy Bullard (back) and Craig Fagan (groin) were passed fit to start.
The visitors, who have scored just once in three away league games this season, had the ball in the net in the seventh minute only to be ruled out for offside.
Cairney unleashed an excellent shot from 25 yards which was parried by goalkeeper John Ruddy. But Jay Simpson's delight at tucking home the rebound was cut short by the linesman's flag.
Norwich squandered a good opportunity to take the lead seven minutes later. Good play from Wes Hoolahan, Korey Smith and Russell Martin forced a corner and from Simon Lappin's cross the ball fell to Leon Barnett, who missed his kick with the goal at his mercy.
Canaries captain Grant Holt, who netted the winner at Preston last Saturday, could not get a proper connection to Lappin's corner and the ball went tamely over the crossbar before Bullard fired well over from 25 yards at the other end.
Ruddy made a comfortable save from Fagan on the half-hour before Barnett headed over from another Lappin corner and Holt's curling effort from 12 yards was easily gathered by Tigers goalkeeper Matt Duke.
Both sides had openings inside the first 10 minutes of the second half with Hoolahan's weak shot from 25 yards going wide and Holt headed over Smith's cross from 12 yards.
For the Tigers, Koren failed to find the target from 25 yards before Bullard's free-kick from range was dealt with by Ruddy.
The best chance of the game came in the 58th minute and it fell to Norwich. Lappin cut the ball back for Hoolahan but his shot from 12 yards was superbly saved by Duke.
Norwich were gradually getting on top and from another surge forward Martin drilled a 25-yard shot wide.
Duke came to Hull's rescue again with 13 minutes left when he denied Chris Martin from 18 yards after he had been put clean through by Hoolahan.
Duke then kept out Barnett's header from a Hoolahan cross before the visitors took the lead with seven minutes left.
The Tigers sealed victory with a second late goal and there was no way back for the Canaries.