The Tigers saw striker Yannick Sagbo dismissed for an alleged headbutt in the 27th minute but it was his involvement in Hull's goal five minutes earlier which proved decisive.
Sagbo was felled in the box by former Hull player Michael Turner and Robbie Brady's coolly converted penalty put the Tigers on their way to their first win back in the top flight.
Norwich were almost permanently camped in the Hull half in the second period but a gallant defensive effort kept them at bay as their woes on the road continue.
Hull will be buoyed by the three points, and the impact of former Tottenham duo Tom Huddlestone and Jake Livermore making their first starts in central midfield.
Scoring goals will no doubt be the issue for the Tigers in the future - Bruce makes no secret that that is going to be his side's chief challenge, for despite finishing second in the Championship last season the Tigers scored five fewer goals than relegated Peterborough.
Considering that statistic, it was no surprise to see Norwich being the more adventurous side in the early stages and debutant Leroy Fer, who was suspended for the opening match of the campaign, putting in a prodigious leap at the far post to meet Steven Whittaker's cross. It looked as though his header was in, but Hull goalkeeper Allan McGregor was relieved to see it miss the upright.
With goals set to be hard to come by, McGregor looks to be an important signing in terms of keeping them out, and he pulled off a full-length diving save to deny Nathan Redmond.
But just as it looked as though it was going to be the Canaries dominating events, Hull began to show some attacking spirit.
The tricky Sone Aluko pulled off a deft backheel which wrong-footed the Norwich defence and left Slovenian skipper Robert Koren clear on goal - but he scooped over and a golden opportunity had gone begging.
The first key event of the match arrive with 20 minutes gone, when former Tigers defender Turner was penalised for a shove on Sagbo as the Ivory Coast international attempted to reach a deep cross.
The contact looked minimal but there were some half-hearted appeals, and more in hope than expectation so there was no little degree of surprise when referee Mike Jones pointed to the spot.
Hull have a dependable penalty expert in Irish midfielder Brady, and he made no mistake as John Ruddy dived the wrong way.
Having won the spot-kick, within five minutes Sagbo found himself sent off for an off-the-ball clash with Russell Martin. Words were exchanged between the pair before Sagbo advanced on his opponent and made contact - also pretty minimal - with his forehead and Jones wasted no time in showing the red card.
That should have been the spark to fire up Norwich but the visitors looked lacklustre with Huddlestone's calming presence in midfield. Aluko, again proving a difficult customer for the Norwich defence, wriggled into space but shot just wide as Hull made light of being a player down to end the half in control.
There was a greater sense of spirit from the visitors in the second half but they appeared to lack that spark of creativity to unlock their opponents' defence.
Jonny Howson twice tried his luck from long range, the first easily collected by McGregor and the second lofted too high, before the Hull keeper produced a save of real quality to keep out Ricky van Wolfswinkel's towering header.
Even in six minutes of injury-time though, Norwich appeared unadventurous, and had Hull had a bit more sharpness they could have wrapped it up in style.