Gary Hooper's fifth goal of the season helped send Norwich above West Bromwich Albion in the Premier League.
The striker scored in the 13th minute with a low drive from 18 yards after Leroy Fer's neat pass.
Fer sealed the points when his shot beat a despairing Boaz Myhill to cap a counter attack in the 89th minute.
It was the Canaries' second away victory of the season and means the Baggies have won just once in nine games.
Norwich's opener in the 13th minute came against the run of play.
Early goal 'critical' says Clarke
Dutch midfielder Fer drifted infield to thread a precise through ball to Hooper and the former Scunthorpe and Celtic striker drove his shot low beyond Myhill and into the corner of the net.
Baggies manager Steve Clarke made five changes to his line-up and gave a first league start to Uruguay defender Diego Lugano in place of the suspended Jonas Olsson.
The hosts enjoyed vast amounts of possession but found John Ruddy in inspired form.
Youssouf Mulumbu's drive from 20 yards and Victor Anichebe's header were both comfortably dealt with by the Norwich keeper.
Nathan Redmond was among Norwich's liveliest performers and he tested Myhill with a dipping free-kick from 25 yards.
Anichebe forced Ruddy into his first meaningful save 11 minutes before the break when the striker collected Mulumbu's pass and sent a swerving effort goalwards from the corner of the 18-yard box.
Clarke introduced strikers Shane Long and Saido Berahino at half-time in an effort to sharpen the hosts' attacking edge but it failed to bare fruit.
Norwich character delights Hughton
Norwich survived claims for a penalty when Stephane Sessegnon's chance was blocked on the line by Martin Olsson.
Sessegnon missed a great chance to equalise when he raced on to Redmond's loose pass but dragged his shot wide when one on one with Ruddy and, as West Brom poured forward, Norwich's potency on the counter-attack grew.
They missed two good chances to double their advantage when Redmond's cutback went behind Johan Elmander and Jonny Howson curled an effort over from 20 yards after good hold-up play by Hooper.
West Brom continued to squander chances.
Sessegnon was denied by the legs of Ruddy from close range after Olsson's stray pass across the face of his own goal, and Long volleyed tamely at the Norwich keeper after Mulumbu's deflected shot fell kindly into his path.
Anichebe sent a diving header wide from Billy Jones' right-wing cross and Brunt's effort from distance was too close to Ruddy.
Long had one last chance to equalise but saw his glancing header brilliantly saved by Ruddy.
After spending much of the second half on the back foot, the visitors sealed the points when Fer carried the ball into the 18-yard box before shooting beyond Myhill.
West Brom head coach Steve Clarke:
"We created a lot of chances but we did not get the goal.
"We made it difficult for ourselves, conceding the goal which came from a throw-in and was a soft goal.
"It gave Norwich something to hang on to. We created enough chances but could not get the goal that would change the game in our favour."
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