Daryl Murphy's stunning half-volley 14 minutes from time kept Sunderland's play-off ambitions on course.
Sunderland had dominated, but Robert Earnshaw almost put Norwich ahead seconds before Murphy's goal, only for Darren Ward to save his curling shot.
Roy Keane's side carved out the clearer chances, with Murphy leading the charge and his winner extended their unbeaten run to five games.
Norwich almost levelled late on, but Liam Miller denied Darren Huckerby.
606 DEBATE: What are your thoughts on this match?
Sunderland manager Roy Keane:
"It was very, very scrappy, but I don't care about that.
"I thought we just about deserved it. There were never going to be too many
goals, it had one goal written all over it.
"It was always going to be difficult and I told the lads they would have to
grind it out.
"We played well in the week (during the 2-1 win at QPR) and could have scored five or six. This was the other way around."
Norwich manager Peter Grant:
"I would have seen a draw as two points dropped. Roy will be delighted with the three points, but I don't think they deserved it.
"We gave a very disciplined performance. It's a big blow for us because when
we play like that we expect to get something from the game.
"I think they were the better team at our place and we were the better team
Sunderland: Ward, Whitehead, Caldwell, Collins, Nyatanga, Stephen Elliott, Miller, Kavanagh, Leadbitter (Yorke 74), Wallace (Hysen 85), Murphy.
Subs Not Used: Fulop, Robbie Elliott, Connolly.
Goals: Murphy 76.
Norwich: Camp, Colin, Shackell, Dublin, Drury, Hughes, Etuhu, Robinson (Eagle 77), Huckerby, Earnshaw, Safri (Thorne 80).
Subs Not Used: Lewis, McVeigh, Ryan Jarvis.
Booked: Shackell, Drury.
Ref: P Joslin (Nottinghamshire).
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