DAVID Dunn was the inevitable hero as his first half penalty gave Rovers all three points at Turf Moor.
The 30-year-old from Great Harwood converted from the spot after Martin Olsson was brought down in the area, sending Brian Jensen the wrong way.
It was Olsson who played an influential role throughout, as he had earlier had a perfectly good goal ruled out, then in the second half he rattled the crossbar with a superb effort that bounced down on the line.
For the home side, their play showed why they are struggling at the wrong end of the table, Leon Cort wasting the home side's best effort in the first half when he volleyed wide, then in the last ten minutes a Fox cross in the final ten minutes flew past Burnley boots in the area.
But it was Rovers' strong defensive display, so often found lacking on the road this season, that earned them the points, Phil Jones again impressive at the back, whilst Gaël Givet returned to great effect at the back.
The final whistle gave way to great scenes as the players celebrated in front of the 2400 blue and white followers, the players throwing their shirts into the crowd with delight.
Ahead of the game Sam Allardyce made two changes from the side that defeated Birmingham City on Wednesday night.
Jason Roberts replaced Nikola Kalinić up front, the Croatian dropping to the bench, whilst the other change saw Gaël Givet return at left back, Keith Andrews missing out with a tight calf.
As is often the case with games of this nature the build-up and the atmosphere at kick-off overshadowed the early proceedings between the two sides.
The first 15 minutes was all about free-kicks, Rovers having two, Burnley one, but neither side made an impression.
But in the 16th minute Rovers had the ball in the back of the net but it was wrongly ruled out. The lively Martin Olsson broke through to latch onto David Dunn's first-time pass to score, but the linesman on the far side had his flagged incorrectly raised for offside.
Two minutes later and there was no doubt that Olsson was onside as he bore down on goal, he took the ball around Brian Jensen in the Burnley goal and went to ground, referee Mike Dean pointed to the spot.
It was a generous decision but David Dunn didn't care as he stepped up to send Jensen the wrong way to put Rovers in front.
Rovers continued to be the better side, Olsson proving to be a real handful with his runs inside from the left. Whilst a timely block stopped Jason Roberts from getting his shot away inside the area after he had turned Cort.
The home fans appealed in vain for a penalty of their own when Samba caught Wade Elliott on the edge of the box, a free-kick was the home side's reward but as was often the case in the first half it came to nothing. Although their best chance did see Alexander pick out Leon Cort in the area but with time he volleyed wide.
Rovers threatened further goals as the first half drew to a close, but Michel Salgado fired wide at the back post, whilst Jason Roberts headed over.
Brian Law's half time team talk must have been ringing in the Burnley player's ears as they started the second period with more purpose.
But with Rovers displaying a more resolute showing at the back in recent weeks they resisted their hosts to very little sight of Jason Brown's goal.
On the break Martin Olsson was deadly, the Swede revelling in his more advanced role due to Givet's return, and he came within inches from doubling Rovers' lead on 67 when he broke free in the area to lash the ball past Jensen, but the ball smashed off the crossbar and down on the line. Replays showed that not all of the ball had crossed the line.
Moments later Olsson was in the thick of the action again, but Jensen saved his right-footed volley. Then Franco Di Santo, whose only goal this term came in the reverse fixture at Ewood, headed wide moments after being introduced.
The final ten minutes saw Burnley try to grab an unlikely leveller, Danny Fox's centre from the left that evaded the outstretched boots of Elliott and Fletcher being their best chance.
Five additional minutes were played, but Rovers saw them out comfortably and as Mike Dean blew the final whilst it sparked tremendous scenes between the players and the visiting supporters as the celebrated in unison.
The win sees Rovers climb back into the top half of the table into 10th place, onto 41 points, the same number they ended with last season with Rovers still having six games remaining.
BURNLEY: Jensen, Alexander (c) (sub Eagles 72 mins), Duff, McDonald, Fletcher, Paterson (sub Blake 59 mins), Elliott, Mears, Cort, Nugent, Jordan (sub Fox 43 mins).
Subs not used: Weaver (GK), Carlisle, Thompson, Cork.
ROVERS: Brown, Salgado (sub Chimbonda 85 mins), Samba (c), Jones, Givet, Diouf (sub Emerton 66 mins), Nzonzi, Pedersen, Olsson, Dunn, Roberts (sub Di Santo 74 mins).
Subs not used: Bunn (GK), Grella, Kalinić, Hoilett.
Booked: Alexander, Fox, Duff (Burnley), Samba, Givet (Rovers).