The Clarets appeared to be on course for a first east Lancashire derby triumph in 34 years after Jason Shackell gave them a deserved first-half lead and Sean Dyche's men were rarely troubled, despite Ben Mee's 65th-minute red card.
But Rovers stalwart Dunn popped up unmarked, and offside according Dyche, inside the visitor's penalty area to produce a clinical finish in the fifth of six additional minutes.
Having been mocked by Burnley's supporters for his tearful reaction to Blackburn's FA Cup quarter-final exit at the hands of Millwall in midweek, the 33-year-old aimed crying gestures at the Darwen End before tearing off his shirt in wild celebration.
This was Dunn's first npower Championship start since October due to persistent calf injuries that have undermined his hopes of gaining an extension to a deal that expires this summer.
"He's a talent," said Appleton. "I think Dunny's one of those people a little bit similar to myself as a person.
"When people want to knock him he always comes out fighting, he always comes up with the answers. That's why I respect him, not only as a player, but as a person as well, because he's probably been written off on many occasions over the last couple of seasons but he keeps coming back.
"I'm delighted for him, as I was for everyone else in the dressing room at the end.
"I had a conversation with him last night at the hotel and we did joke about potential new contracts. I said it depends what you do over the next 10 games and how many games we win.
"He did remind me of that, as you can imagine, as we were going into the dressing room when he jumped on my back."