Two first-half goals from Stephen McPhee did the damage and, although Jamie Cureton gave the home fans something to cheer with a second-half penalty, the visitors ran out worthy winners.
Norwich kicked off attacking the River End goal, but failed to create any chances in the first quarter of an hour.
David Marshall blocked a snap-shot from Andy Morrell, but when Gary Taylor-Fletcher crossed the ball back in from the right, McPhee was running in at the far post to beat Marshall with a close-range header.
For the next 15 minutes the visitors kept the home side pinned back in their own half.
Just before the half hour, Wes Hoolahan released McPhee but his shot went wide as Marshall narrowed the angle.
It was ten minutes from half-time before Norwich fashioned a goal attempt, but Dion Dublin's header from Darren Huckerby's cross flashed wide.
Huckerby was then tripped as he then broke into the Blackpool penalty area, but referee Rob Shoebridge angered the home fans by waving play on.
With Mark Fotheringham down with a head injury, once again Mr Shoebridge allowed play to continue and McPhee took full advantage by racing clear of the City defence and beating Marshall to his right with an angled drive from 18 yards.
The Norwich Captain had to be stretchered off and was replaced by Matty Pattison.
Deep in stoppage time, Cureton fired wide when Dublin's header set him up.
Early in the second half, Cureton was pushed over but still Mr Shoebridge dismissed penalty appeals.
Marshall saved McPhee's shot while at the other end Paul Rachubka made a save from Huckerby.
At the third time of asking, the referee did award Norwich a penalty for a foul by Shaun Barker on Pattison and Cureton's right-foot shot beat Rachubka low to his right.
Substitute Ched Evans had a shot saved by Rachubka and that was as close as the Canaries came to taking anything from a game bossed by the Tangerines.