A Robbie Brady spotkick in the 22nd minute proved the game’s only goal, but the hosts were under the cosh for the best part of an hour after Yannick Sagbo was dismissed on the half-hour mark for a headbutt on Canaries skipper Russell Martin.
But Bruce’s side held firm and afterwards he spoke of his pleasure with the win.
“We are obviously delighted to get up running, it was vitally important,” he told the BBC.
However opposite number Chris Hughton was aggrieved with the penalty decision.
He said: “I thought the penalty was soft. If you are going to give that as a penalty then you are going to give so many of them in every game.”