Second-half goals from Alexander Tettey and Cameron Jerome’s double lifted the Canaries two points above Nottingham Forest – for 24 hours at least – but Brentford will wonder how on earth they came away with nothing.
The newly-promoted hosts would have gone above Norwich with a win and could have been three or four goals ahead after a one-sided first half.
But City somehow held out until half-time, and then broke away ruthlessly to snatch the points after the interval.
It was harsh on Brentford, who paid for a defensive lapse when Tettey hit the opener and complained they should have had a penalty moments before Jerome headed the second.
They could do nothing about the third, though, with Jerome unleashing a thunderous shot from 25 yards to seal the victory.
Bees striker Andre Gray, who was turning out for Luton at Wrexham in the Conference this time last year while Norwich were playing Tottenham in the Premier League, could easily have had a first-half hat-trick.
He was inches away from touching Stuart Dallas’ cross into an empty net, before turning and firing inches wide and seeing another shot deflected past the post by Jos Hooiveld..
City keeper John Ruddy kept the scores level with a flying save to prevent Alan McCormack’s 20-yard drive from nestling into the top corner and also kept out Alex Pritchard’s close-range effort.
And moments before the interval McCormack again came agonisingly close to breaking the deadlock with a low drive which beat Ruddy but flew just wide.
But Norwich looked a different side after the interval and broke the deadlock in the 68th minute when James Tarkowski was caught in possession in his own half and Wes Hoolahan laid the ball across for Tettey to slot home.
There was controversy five minutes later when Hooiveld appeared to foul Pritchard in the area but nothing was given, and Norwich immediately broke away again with Cameron diving to head in Steven Whittaker’s cross.
And Cameron wrapped up the win in style seven minutes from time when he rifled in a stunning third to keep the Canaries flying high in their bid to return to the Premier League.