Substitute Johann Berg Gudmundsson scored for the first time in 20 months to give the Clarets the lead with little over a quarter-of-an-hour remaining in the Midlands.
But the away side’s lead last just six minutes as Scott Hogan tapped home unchallenged from close range after George Hall had got away down the right hand side to tee up the striker.
It was a 12th game unbeaten in the Championship for Vincent Kompany’s side, who are now third in the table after returning 26 points from 15 games.
Here are the ratings.
1. Arijanet Muric 6
Another 90 minutes without really being tested, but nowhere near Tahith Chong's set-piece when Auston Trusty almost capitalised in the first half. Combined well with Charlie Taylor to snuff out striker Scott Hogan from close range. Photo: CameraSport - Andrew Kearns
2. Connor Roberts 6
Managed to get by Emmanuel Longelo on a few occasions in the first half, picking out Vitinho with a peach of a pass in one instance. Conceded a number of set-pieces down his side of the pitch, which allowed the hosts to impose their height advantage inside the penalty area but, other than that, looked defensively sound. Photo: CameraSport - Andrew Kearns
3. Taylor Harwood-Bellis 7
Might have done better with a free header from Anass Zaroury's delivery in the first half, but another solid showing from the England Under 21 skipper. Showed he was up for the challenged when faced with an opponent of Troy Deeney's ilk, making a fine intervention to prevent the veteran from countering in the second half, and then diverted a Scott Hogan header off course. Photo: CameraSport - Andrew Kearns
4. Charlie Taylor 6.5
Stood up well when the Blues turned over possession in threatening areas and made a vital block to prevent Scott Hogan from getting a shot away late in the first half. However, couldn't get back quickly enough to prevent substitute George Hall from picking out Scott Hogan for the equaliser. Photo: CameraSport - Paul Greenwood