Town dropped to seventh after Derby drew 2-2 at home with 10-man Watford in this evening’s later game.
The Hornets went ahead through Matej Vydra in the 23rd minute but had Marco Motti red-carded just before the break, ex-Blue Darren Bent netting the resultant penalty.
Tom Ince put Derby in front 12 minutes after the break but Odion Ighalo levelled in the 75th minute.
The Rams are now sixth on 68 points, ahead of the Blues - by 10 - and eighth-placed Wolves - by 14 - on goal difference.
Brentford are in fifth on 69 points, Watford fourth on 73, Norwich ahead of the Hornets in third on goal difference, with Bournemouth second (74) and Middlesbrough (75) top.