Robbie Blake stunned the home side with a brilliant strike early on, but then goals from David Dunn, Franco Di Santo and Pascal Chimbonda ensured the local bragging rights belonged to Rovers.
In the end, Burnley boss Owen Coyle could have few complaints about the final outcome, even though there was an element controversy about Rovers' second goal.
This was Rovers' third home victory of the season and Sam Allardyce's side generally looked the more accomplished side over the course of the 90 minutes.
Any thoughts of this derby being a typically cagey affair were blown out of the water by two goals in an explosive first nine minutes.
Burnley stunned the home fans into silence when they scored their first away goal of the season in the Barclays Premier League in the fifth minute.
A Rovers attack broke down and Wade Elliott promptly set Blake racing away on a counter.
As the home defence backed off, Blake cut inside and unleashed an unstoppable right-foot shot from just outside the area which rocketed past a startled Paul Robinson.
However, the Clarets' joy was to prove short-lived as Rovers were behind for just four minutes before Dunn restored parity.
Morten Gamst Pedersen picked out Di Santo with a cross from the left and the his cushioned lay-off dropped invitingly for Dunn, who swept a first-time shot past Brian Jensen and into the bottom corner from ten yards out.
Suddenly, Rovers' tails were up and they almost snatched a second four minutes later, but El Hadji Diouf dragged his shot wastefully wide of the far post.
Burnley's reprieve proved only temporary, however, as the home side did snatch a second - somewhat controversially - in the 21st minute.
Dunn floated a free-kick towards the far post, which was headed back across goal by the towering Chris Samba.
As Jensen came to claim it, he appeared to get nudged in the back by Di Santo, but referee Chris Foy played on and Graham Alexander then made a hash of an attempted clearance, leaving Di Santo to head home from three yards out.
Things got even better for the home side three minutes before half-time when Chimbonda outfoxed a defender in the area before curling an exquisite shot past Jensen to make it 3-1.
The second half lacked the breathless excitement of the first.
Burnley's record signing Steven Fletcher had an early chance to reduce the deficit but failed to hit the target.
After that, the Clarets rarely looked like mounting a comeback, until substitute Chris Eagles grabbed a late consolation in injury time.