Dunn cancelled out an opener from Robbie Blake before Franco di Santo and Pascal Chimbonda added further strikes, with substitute Chris Eagles netting a late second for Burnley.
But with Premier League fixtures against Chelsea and Manchester United up next, the midfielder was more interested in the points than beating Blackburn's local rivals.
"To score against Burnley was great but more important than that was to get the three points," the man of the match told Sky Sports.
"Our next couple of games are really difficult so it's great to get 10 points before we play those matches.
"But you could see by the reaction of the fans at the end how much this meant."
The crowd chanted 'Dunny for England' but the 29-year-old was cautious over his chances of adding to his solitary England cap, won in 2002.
"Who knows? It's difficult to get in the England team given the amount of quality players they have," he said.
"I'll keep doing my best for Blackburn. You never know."
Sam Allardyce was full of praise for a tremendous performance from his Rovers side, telling Sky Sports: "We are very pleased for ourselves first and foremost, but for the fans as well
because there was terrific support.
"It was a wonderful performance and a wonderful result coming from behind, with some excellent quality goals.
"Often derby games can pass by as ordinary games in terms of the football that is played but I don't think you can complain about the quality of the goals.
"It is a great three points bearing in mind this was a local derby and bearing in mind our next two fixtures are Chelsea away and Manchester United away."
Dunn produced another sparkling display in support of main striker Di Santo and Allardyce was impressed with both players.
Speaking about Dunn, Allardyce said: "We have dropped him in that little position, we have got him fit and now we have got some terrific performances out of him.
"Franco also contributed well for the first goal and got one himself, so those two were terrific for us."