The Coca-Cola League One side, under new boss Paul Lambert, were undone far too easily on the break as Teemu Tainio set the ball rolling for the Barclays Premier League club, before Andy Reid netted a well-taken double.
Wes Hoolahan reduced the deficit just after the hour, only for Owain Tudur Jones to deflect a corner into his own net minutes later, before Norwich finished with nine men when last man Michael Spillane was sent off for a professional foul on Frazier Campbell, and keeper Ben Alnwick suffered a cut to his face.
It looked like Norwich could take advantage during the early exchanges and the home fans were calling for a penalty after just six minutes when Nyron Nosworthy bundled over teenage striker Luke Daley, although referee Anthony Taylor was unimpressed.
Sunderland, though, looked dangerous on the break and took the lead in the 26th minute when Kenwyne Jones brushed off the challenge of Gary Doherty before darting into the right side of the penalty area and cutting the ball back to Tainio, who drilled in a low shot from 10 yards.
It was 2-0 moments later when Reid chipped exquisitely over Alnwick into the far corner
The third goal came in the 36th minute when Campbell played in Reid to finish off a sweeping move, as Norwich were once again torn apart on the break.
Norwich upped the tempo at the start of the second period and their pressure paid off in the 63rd minute when Jon Otsemobor's cross from the right was headed against the far post by substitute Cody McDonald - and Hoolahan knocked the ball into an unguarded net.
However, any thoughts of a comeback were quickly ended when Tudur Jones deflected a corner into his own net.
Spillane, as the last defender, was sent off in the 82nd minute for pulling back Campbell, who slid into the keeper and Alnwick had to go off for treatment to a cut face, meaning McDonald spent the closing minutes as a make-shift goalkeeper as the Canaries had already used all three substitutions.