The Canaries were no match for their Premier League opponents who made easy work of their 4-1 victory at Carrow Road.
Teemu Tainio broke the deadlock with his first Sunderland goal on 25-minutes after picking up on a superb ball through from Kenwyne Jones.
The Finnish midfielder was completely unmarked on the left-hand-side and needed just a simple tap-in to notch his first goal for the Black Cats since his move from Spurs last year.
Just minutes later, the visitors were two-goals to the good after Jones, again, set up Andy Reid for a sublime chip over keeper Ben Alnwick.
Reid then secured a brace just after the half-hour mark after picking up on a timely through-ball from Fraizer Campbell to slot home from close range.
Norwich looked to be coming back into the game in the second half, netting just after the hour mark through Wesley Hoolahan.
Soon after - substitute Chris Martin managed to steer Simon Lappin's decent cross just wide of the far post.
The crowd appeared to be lifted by the Canaries sudden surge towards goal, albeit temporary as Owain Tudur Jones managed to slot the ball into his own net to make sure of Sunderland's progression through to the third round.
Norwich finished with only nine men when defender Michael Spillane was sent off for a professional foul on Frazier Campbell, and keeper Ben Alnwick suffered up a cut to his face.
ChangesCraig Gordon came into goal, with only captain George McCartney and striker Kenwyne Jones retaining their places from the side which beat Blackburn.
It looked like Norwich could take advantage during the early exchanges. The home fans - in a crowd just over 12,000, well short of that for the game against Wycombe on Saturday - were calling for a penalty after just six minutes when Nyron Nosworthy bundled over teenage striker Luke Daley.
Referee Anthony Taylor, though, was unimpressed.
Sunderland looked dangerous on the break. On 12 minutes, Reid whipped the ball over, which Campbell turned goalwards with a stunning over-head effort. On-loan Tottenham keeper Alnwick got his fingertips to the rasping shot, which was just enough to tip it onto the crossbar.
Norwich were riding their luck, but broke clear when Simon Whaley went into the right side of the penalty area. However, his weak shot was saved by Gordon.
The Scottish keeper was then called on again to touch over Simon Lappin's long-range strike.
Sunderland took the lead on 26 minutes. Jones brushed off the challenge of Doherty before darting into the right side of the penalty area and cut the ball back to Tainio, who drilled in a low shot from 10 yards.
Before Norwich had a chance to respond, it was 2-0. Sunderland broke away down the left through Reid.
From just inside the box, the winger chipped a perfectly-weighted ball over the keeper and into the far corner.
It was then 3-0 on 36 minutes as Norwich were once again torn apart on the break.
A string of one-touch passes picked out Campbell in the middle, who in turn fed Reid on the overlap, and he drilled the ball into the top corner.
At the end of the first half, Gordon saved well from Tudur Jones, the Wales midfielder drilling in a low shot from 15 yards.
Sunderland replaced Jones with Daryl Murphy for the second half. Norwich upped their tempo following the restart.
In the 63rd minute, Norwich's pressure finally paid off. 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.
Chris Martin then just failed to connect with a low cross at the far post. 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 on 82 minutes for pulling back Campbell, who slid into the keeper and Alnwick had to go off for treatment to a cut face.
With all three substitutes used, McDonald went in goal. However, he could do little but watch Carlos Edwards crash a 25-yard shot against the bar.