Wes Hoolahan had headed Norwich into the lead before Bunn saw red for handling outside his box, with Sunderland then levelling from the penalty spot before the break through Craig Gardner after Sebastien Bassong was adjudged to have handled.
Norwich broke the deadlock in the 26th minute after some dismal defending from Sunderland, as they allowed Kei Kamara a free header inside the six yard box from Robert Snodgrass' corner, with Hoolahan diverting the ball home from virtually on the goalline.
The tension inside the stadium increased as the Black Cats fell behind, but just four minutes later the visitors were reduced to 10 men when Bunn raced from his area to deny Danny Graham after Michael Turner's poor back-header, with the ball striking his chest and arm.
Referee Chris Foy had no hesitation despite Bunn's furious protests and those of his team-mates, with replays showing the official made the right call, with Lee Camp coming on for the Canaries and goalscorer Hoolahan the outfield player to be sacrificed.
Camp was then rooted to the spot as Gardner's resulting free-kick whistled inches wide of the post, but he could do nothing about Sunderland's equaliser in the 40th minute, with Norwich again left infuriated by the decision-making of the officials.
John O'Shea's hopeful ball into the box struck the chest of Bassong and rolled down his outstretched left arm, with Foy acting on the advice of his assistant who had a perfect view. Gardner showed great composure to find the top corner from 12 yards to level the scores.
Sunderland twice came close to taking the lead before the break as Graham skewed wide after Camp had pushed away Sebastian Larsson's pile-driver, before Danny Rose struck the outside of the post via a deflection off Turner with the last kick of the half.
Sunderland were on the front foot immediately in the second half, with Stephane Sessegnon given a free role and Gardner very advanced on the right, and the latter warmed Camp's fingers in the 59th minute with a stinging drive after being set up by Fletcher, while Mignolet had to be alert to clear from outside the box with Kamara bearing down on goal.
Norwich then had reason to feel aggrieved with Rose penalised for handball, with replays showing he was clearly inside the area, rather than outside as Russell Martin's cross struck his arm, but Foy gave a free-kick on the line.
Substitute Grant Holt had a great chance to give the visitors the lead when substitute Titus Bramble completely misjudged a long ball forward, but the striker's first touch was far too heavy and allowed Mignolet to gather, with the Canaries captain booked for lunging in on the keeper.
Despite their numerical advantage, Sunderland failed to test Camp with any regularity, with Sessegnon hooking a good chance wide late on, and Martin O'Neill's men have now taken just three points from seven games with fixtures against Manchester United, Chelsea and Newcastle on the horizon.