The former England midfielder, making his first league start since October due to persistent calf problems, showed a cool head to dispatch a loose ball in the Clarets box into the net, after five of six scheduled additional minutes.
Jason Shackell had converted Ross Wallace's 32nd-minute free-kick at the second attempt to give Burnley the lead but Blackburn pressed either side of Ben Mee's 64th-minute dismissal for two quickfire bookings.
The opening period was interrupted by a home supporter releasing a chicken onto the field in protest against the regime of Rovers' poultry magnate owners Venky's but after that Blackburn poured forward and striker Jordan Rhodes was left with a bloodied nose when he took a boot to the face from Burnley centre-back Michael Duff.
Rovers goalkeeper Jake Kean was forced into a magnificent 19th minute save - touching over when Charlie Austin teed-up Martin Paterson. Austin blasted wildly off-target to conclude a clever routine from the resulting corner in unsatisfactory fashion.
The game started to drift as the early intensity tailed off and it was Burnley who capitalised. Marvin Bartley, a bustling influence at the heart of the visitor's midfield, was fouled by David Jones 40 yards from goal and Shackell slammed home after his initial header from Wallace's floated delivery came back off the post.
Burnley instantly looked to press home their advantage with Rovers reeling, and Wallace came agonisingly close with 30-yard free-kick that clipped the upright.
Just as Burnley were starting to look comfortable, Mee's heavy touch on a run forward from left-back saw him career into Grant Hanley and earn a second booking six minutes after a late challenge on Dunn.
It might have been 10-a-side when Hanley, carrying a first-half yellow card, brought his hand across Kieran Trippier's face when chasing a punt forward.
Aside from a couple of frantic goalmouth scrambles, Burnley were largely untroubled until Cameron Stewart's chipped ball into the box was touched on by Jason Lowe and the unmarked Dunn clinically drove past Lee Grant left footed.
Source: PA