The hosts looked for an immediate equaliser as Graham charged towards the Norwich goal, one-on-one with Bunn.
Bunn rushed out of the penalty area to prevent the shot, but the ball struck him on the arm outside of the box, resulting in Chris Foy showing the Norwich keeper a red card.
Chris Hughton took off the goalscorer in order to bring on Lee Camp for his first appearance for the club.
Things got worse for the visitors when Sunderland were awarded a penalty after the assistant referee ruled that Sebastien Bassong had handled the ball, with Craig Gardner stepping up to take the spot kick and level the scores for the Black Cats.
Sebastian Larsson almost gave the hosts the lead just before half time, when his powerful strike from long range was only cleared as far as Graham, but the former Swansea striker scuffed the ball wide.