It was a comfortable victory as well for Sam Allardyce's side after an early scare when Robbie Blake made the breakthrough for Burnley after five minutes.
However the home side effectively sealed the points before half-time thanks to goals from David Dunn, Franco di Santo and Pascal Chimbonda.
Substitute Chris Eagles scored a second for Burnley in stoppage time but they have now lost five successive games on the road in the Premier League this season.
Blackburn's win gave their manager Allardyce an early birthday present as he is 55 on Monday.
Burnley got off to the best possible start when Blake scored after Chris Samba had cleared the crossbar for the home side.
Blake picked up the ball just beyond the halfway line and raced forward as Blackburn backed off. He took advantage of the space on offer to deliver a thunderous strike from 25 yards beyond Paul Robinson that flew into the corner.
It was reminiscent of his goal against Manchester United earlier in the campaign and gave Burnley the boost they were looking for.
The Clarets' lead was short-lived however as Blackburn equalised in the ninth minute following a flowing move.
Morten Gamst Pedersen crossed the ball into the area and a clever flick by Di Santo released Dunn and he scored from close range.
It was an open game and El-Hadji Diouf squandered a good chance six minutes later by sending his shot across the face of the goal after being set up by Steven Nzonzi.
Blackburn went ahead in the 22nd minute when Di Santo took advantage of Graham Alexander's misplaced clearance although there was a question mark over whether goalkeeper Brian Jensen was impeded one of his own players.
It was Argentinian striker Di Santo's first goal for the club - and a welcome one at that - since his arrival on loan from Chelsea.
However the way he celebrated in front of the visiting supporters did not go down well with referee Chris Foy and he was booked.
Given their dismal away record on the road this was a difficult time for Burnley after Di Santo's goal.
Blackburn stepped up the pace and Dunn worked himself into a good position in the 37th minute only to send a soft shot into Jensen's arms.
Jensen then had to look alert to take a header from Samba after Dunn had swung in a free-kick from the left four minutes later.
Blackburn extended their lead in the 43rd minute with a splendid goal that cut the visitors apart.
Keith Andrews picked out Pedersen on the left and he released Chimbonda on the overlap.
The former Tottenham full-back got away from Steven Fletcher and cut into the area before finding the corner with his effort.
Burnley were anxious to get back in the game and Fletcher dragged a shot wide of the post in the 50th minute after linking up with David Nugent.
Play switched down the other end and the impressive Di Santo skipped away from Steven Caldwell, only for Tyrone Mears to clear for a corner.
Burnley kept pushing forward and Eagles tested Robinson with a minute to go, only for the goalkeeper to push the ball around the post.
Former Manchester United man Eagles pulled a goal back in stoppage time, scoring from close range following a cross from Stephen Jordan.
Jensen was booked in the final moments after racing from his area and flooring substitute Jason Roberts as he attempted to get clear.