The Glaswegian turned the ball home from close range with 12 minutes remaining after Peter Whittingham's cross caused confusion in the Derby defence.
Michael Chopra had earlier put Cardiff ahead after 15 minutes with a tidy 12-yard finish.
The lead lasted just 10 minutes as Tomasz Cywka poked home his first goal in English football to equalise for the Rams.
Cardiff had the first chance of the game in the 11th minute. Derby skipper Robbie Savage gave the ball away to Whittingham, who found Chopra on the right.
Chopra cut the ball back for Whittingham and his first-time shot from 15 yards was just over the bar.
The visitors took the lead four minutes later when Kris Commons was dispossessed by Burke, who picked out Chopra and the striker smartly took his time before beating Stephen Bywater.
Derby equalised in the 25th minute. John Brayford's throw into the box was chested down by Luke Varney who hooked the ball over his head. Cywka timed his run perfectly to steer a low shot past David Marshall from eight yards.
Cardiff broke swiftly in the 33rd minute with Jay Bothroyd finding Burke, who cut in from the right and saw his shot beaten behind by Bywater.
Four minutes before half-time, Commons' corner dropped to the unmarked Cywka but his volley was too close to Marshall.
Following that chance, Kevin McNaughton worringly went down and there was a lengthy delay as he was attended to by medics before leaving the field on a stretcher.
Daniel Drinkwater shot over the crossbar on the hour mark before Derby responded through Paul Green, whose shot was saved by Marshall.
Burke then converted Whittingham's cross after Bywater and one of his defenders appeared to get in each other's way.
Shaun Barker could have rescued a point for the Rams but the ball struck the big defender on the knee as it bobbled around inside the six-yard box.