The midfielder picked up the man-of-the-match award by capping an impressive performance with his fifth goal of the season.
Dunn cancelled out Robbie Blake's opener and Blackburn kicked on with Franco Di Santo and Pascal Chimbonda also finding the target before half-time.
Substitute Chris Eagles pulled another goal back for the visitors in stoppage time but they have now lost five successive league matches on the road.
Allardyce was delighted at the manner of the victory and Dunn's performance.
He said: "The first thing we had to do was to secure a fit David Dunn so he could be selected regularly.
"Then he had to work out what he had to do on his own when everyone else had disappeared from the training ground.
"We have also found him a position that suits, playing just off the front man and he is playing better than he has for a long time.
"He is not only our leading scorer but he is providing others the opportunity to get goals. He is doing a terrific job.
"Dunny can change games and put us back in contention against Burnley very early.
"That was important from our point of view. It wasn't an easy finish from him but he made it look easy."
With Premier League fixtures against Chelsea and Manchester United next, Dunn 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," he 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."
Burnley manager Owen Coyle complained about Blackburn's second goal from Di Santo as he felt goalkeeper Brian Jensen had been obstructed.
Coyle said: "I was convinced that Di Santo had moved into Stephen Jordan and did enough to put Brian Jensen off. That was my initial thought and you won't convince me otherwise.
"Those marginal decisions are going against us. But referees do the job to the best of their ability and I am not going to get caught up in that. We just have to get on with it."
Coyle added: "We got off to a great start and it was a terrific goal from Robbie then we conceded some soft goals.
"We have scored two goals but got no points. However that away win is around the corner - we will continue to play on the front foot as that is what our fans deserve."