Robert Earnshaw's second-half goal was enough to settle a scrappy affair at Carrow Road.
Norwich keeper Paul Gallacher stopped Sunderland opening the scoring as he got down well to parry David Connolly and Tobias Hysen's efforts.
Despite Sunderland's dominance, Norwich took the lead on 51 minutes when Earnshaw drove in Paul McVeigh's cross.
Sunderland appealed for a penalty late on when Dion Dublin appeared to foul Daryl Murphy but were waved away.
Norwich boss Peter Grant on Dion Dublin:
"It was a good job Dion was playing, because if he was not, we would have lost the game.
"There is no doubt in my mind about that - especially in the second half when he defended the box with his life.
"He was colossal for us in everything he did, his organisation, guiding people about him. I am delighted to have him about the squad."
Sunderland boss Roy Keane:
"We deserved something out of the game - but that is the beauty of football I suppose, that you do not always get what you deserve.
"We just have to lick our wounds and get ready for next week."
"The determination and the effort was there, and at half-time I thought we were comfortable. But that is a dangerous word to use in football."
Norwich: Gallacher, Colin (Eagle 84), Shackell, Dublin, Drury, Etuhu, Safri, Robinson, McVeigh (Hughes 74), Earnshaw, Huckerby.
Subs Not Used: Ashdown, Thorne, Spillane.
Booked: Gallacher, Huckerby.
Goals: Earnshaw 51.
Sunderland: Ward, Whitehead, Danny Collins, Caldwell, Nyatanga, Lawrence, Kavanagh (Leadbitter 72), Yorke, Hysen (Murphy 68), Brown, Connolly (Stephen Elliott 77).
Subs Not Used: Alnwick, Nosworthy.
Booked: Caldwell, Kavanagh.
Att: 24,652.
Ref: M Riley (W Yorkshire).