In the fifth minute of added time, Dunn was on hand to score his first goal since October and claim a valuable point after Jason Shackell had earlier put the Clarets ahead.
The dramatic finale was certainly timely for Dunn, who is out of contract in the summer, after his manager Michael Appleton recently challenged the midfielder to prove his worth to Rovers.
Dunn told the club's official website: "If you get in the right areas and if you keep doing the right things over and over again then things happen for you.
"I don't think it was luck that it landed to me in the box, I thought it was fate and I was always going to score that."
He added, "We managed to show a lot of composure and a lot of courage to get on the ball and play. It was all good."