Dunn popped up unmarked inside the visitors' penalty area before producing a clinical finish in the fifth of six additional minutes.
The Clarets had 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.
It was Dunn's first 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 ten 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."
Appleton revealed he ignored the concerns of his backroom team over Dunn's capacity to complete a gruelling 90 minutes.
"The coaching staff behind me kept saying, 'We might have to be careful with Dunny, we don't want him injured'.
"And I'm thinking, 'No, no, no - if anyone's going to unlock the door with a pass or create something then surely it's going to be Dunny.
"It was adrenaline and the fact it was against Burnley - his passion towards that club to play for this club was probably the thing that made sure I kept him on the field."