In a match between two candidates for relegation, it was Sean Dyche's men who took all three points, as QPR remain pointless on their travels in the Premier League this term.
Scott Arfield struck the first blow with a fine solo goal, only for former Burnley striker Charlie Austin - who scored and was sent off in QPR's 2-0 win in the reverse fixture in December - to level from the penalty spot.
Burnley led at the break, though, thanks to a calm finish from Danny Ings and that proved enough.
The hosts saw Ings again go close after the break, while Ashley Barnes had a goal disallowed to ensure nerves remained frayed throughout.
Victory lifts Burnley to 16th, while QPR drop into the bottom three.
Burnley named the same XI for the seventh Premier League match in a row, while QPR recalled Adel Taarabt for the first time in almost exactly a year.
Blustery conditions at Turf Moor played a part in a tepid opening, but the match came alive in the 13th minute thanks to a fine solo effort from Arfield.
The midfielder collected the ball on the left flank and he skipped past the challenges of Eduardo Vargas and Richard Dunne before curling his shot into the far corner.
QPR sought a response and the visitors were unlucky not to be level when Austin scooped Mauricio Isla's cut-back from the byline onto the right-hand post.
However, Austin would not be denied in the 33rd minute when the striker won a penalty after going to ground under a lazy challenge from Dean Marney.
The striker picked himself up to drill his effort into the bottom left-hand corner, much to the chagrin of supporters who used to hold him in such high regard.
QPR's parity lasted just four minutes, though, as Ings restored Burnley's lead.
The forward showed expert control to collect Barnes' long ball before twisting past two challenges and coolly slotting past Green.
Burnley almost scored a third seven minutes after the break when a quick throw-in caught QPR off guard and Arfield's half-volley produced a smart stop from Green.
At the other end, Steven Caulker saw claims for handball against Michael Keane in the penalty area dismissed by referee Andre Marriner.
Ings' then flashed a shot wide from a quick Burnley break, before Barnes bundled home from a corner - only to see the goal chalked off for a foul on Green.
Green again prevented Burnley adding gloss with a superb point-blank stop from Keane's back-post header, before opposite number Tom Heaton made a terrific fingertip save from Caulker's header in injury time to preserve the precious points.
