Yannick Sagbo won the first-half spot kick before being sent off after 26 minutes and Chris Hughton's Canaries were unable to take advantage of their numerical superiority
Robbie Brady's first-half penalty was the difference between the two sides, while Yannick Sagbo's red card five minutes later left the hosts hanging on in the second half.
|By Joe Doyle
Hull picked up their first points of the season thanks to an impressive defensive display, with James Chester, Curtis Davies and Tom Huddlestone all putting in good performances.
Following Robbie Brady's penalty and the red card for Yannick Sagbo, Norwich will be extremely disappointed not to leave with at least a point. They worryingly did not create chances and were set out too defensively against a team they should be dominating.
Nathan Redmond looked like the only player capable of creating anything for the visitors, and they will have to offer much more support to Ricky van Wolfswinkel if they are to get the best from the striker.
Norwich also made two changes from their previous fixture, with the injured Elliott Bennett replaced by Alexander Tettey and Leroy Fer coming in for Wes Hoolahan.
The visitors had the better of the opening 10 minutes as Fer headed Steven Whittaker's cross over before Nathan Redmond stung the palms of Allan McGregor with a fierce drive from distance.
As Hull worked their way back into the game, Sagbo released Livermore into the area with a clever back-heel but the Tottenham loanee fired over the crossbar with his left foot.
Sagbo was again instrumental as Bruce's side took the lead from the penalty spot on 22 minutes. Former Hull defender Michael Turner wrestled the Ivorian to the floor in the six-yard box as he tried to reach Ahmed Elmohamady's cross from the right and Brady stepped up to send John Ruddy the wrong way and break the deadlock.
Sagbo's eventful afternoon was soon finished, however, as he was dismissed by referee Mike Jones for an off-the-ball clash with Jonny Howson, appearing to headbutt the Norwich midfielder.
As the hosts focused on getting to half-time with the lead, chances were at a premium. Sone Aluko curled an effort beyond Ruddy's left-hand post, while Redmond fizzed a 25-yard free kick just wide of goal with the last action of the half.
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Five minutes later, the midfielder took aim once more but this time his effort from distance flew over the crossbar.
Norwich continued to press. Redmond fed Ricky van Wolfswinkel, whose neat lay-off was lashed high and wide by Tettey from the edge of the box as Norwich became frustrated.
The visitors were brilliantly denied by McGregor with 20 minutes to go, the Scotland international leaping to tip Van Wolfswinkel's powerful header over the bar.
Norwich continued to dominate possession in the final stages but failed to create any further chances as Hull doggedly held on for their first points of the season.