Former England striker Andy Cole rolled back the years with a hat-trick, as Rangers tasted defeat at Loftus Road for the first time in 2008.
Trailing 2-0 inside the opening half hour, Owen Coyle's men came back from the dead to win 4-2, in an extraordinary Championship encounter.
Gavin Mahon's first goal in 10 months put Rangers in front early on and when Patrick Agyemang made it two in the 30th minute, the R's faithful sensed another comfortable home win.
But Burnley had other ideas and thanks to Cole's deadly treble and a close range header from Ade Akinbiyi, the Clarets exacted revenge for the R's 2-0 win at Turf Moor in December - and in some style too.
Luigi De Canio welcomed back international duo Damion Stewart and Akos Buzsaky, after the pair were rested for Saturday's 3-2 victory at St Mary's.
Michael Mancienne and Kieran Lee dropped to the bench, while US goalkeeper Matt Pickens was also named amongst the substitutes.
Cole retained his place in the Clarets' starting XI after opening his account against Colchester United on Saturday, while highly-rated attacker Kyle Lafferty returned.
Rangers enjoyed the better of the opening exchanges, with Hogan Ephraim firing wide on six minutes, after he latched on to Buzsaky's inch-perfect cross-field pass.
To their credit though, Burnley more than held their own as the clock ticked towards the quarter hour. Lafferty's pace and guile caused Matthew Connolly all sorts of problems early on, with the wide midfielder twice delivery teasing balls into the heart of the R's six-yard box, which the returning Stewart mopped up with ease.
But it was the R's who continued to pose the greater threat in the attacking third and their forward-thinking policy was rewarded in the 14th minute, thanks to a first goal in Rangers colours from Mahon.
Lee Camp's perfectly flighted free-kick found Buzsaky, and when his deft flick on fell at the feet of Agyemang, the in-form front-man played a sublime back heel into the midfielder's path.
With time to look up, the Magical Magyar crossed to the back post and picked out the arriving Mahon, who leapt above a static Clarets rearguard to nod home his first goal of the campaign.
It was all one-way traffic by now, and Rangers doubled their advantage on the half hour. Guess who got it? Yes, you guessed it - that man, Agyemang!
But the credit for the goal had to go entirely to Damien Delaney, who having picked up possession on the edge of his own box, raced fully 60-yards before playing a defence splitting through ball into the path of the R's top-scorer.
Baring down on goal, Agyemang had the coolness to drop a shoulder, round Jensen and tap the ball into an empty net for his eighth goal in six Championship matches.
The R's nearly added a third sixty seconds later, as Buzsaky fired wide from distance, before Zesh Rehman's marauding run ended with his speculative left footed curler being palmed away by the now over-worked Clarets custodian.
The workmanlike Martin Rowlands was forced off six minutes from the break, with a hip injury. Mikele Leigertwood entered the fray as a consequence, with Mahon taking over the captaincy duties.
Leigertwood was on the pitch just a matter of seconds when the R's conceded a first goal at home since New Year's Day.
Joey Gujonsson's free-kick appeared to be drifting well wide of Camp's right hand post, until Cole stuck out a leg and inadvertently thrashed the ball into the roof of the net.
Ephraim twice tested Jensen early in the second half, but the Clarets keeper came out on top on both occasions.
Burnley refused to lie down though and when half-time substitute Ade Akinbiyi floated a neat ball to the far post, Cole dispatched the ball with aplomb to make it 2-2.
Undeterred, Connolly almost restored the R's one goal buffer four minutes later, when his dipping 25-yard volley brought the very best out of Jensen.
Play soon switched to the other end, and this time it was Camp's heroics that kept the scores level, as he dived full stretch to tip Wade Elliott's piercing drive onto the outside of the post.
The action was relentless, with Vine dragging a 15-yard effort wide moments later and Leigertwood forcing Jensen to smother the ball at this near post in the 73rd minute, as the R's continued their all-out pursuit for the all-important fifth goal of the contest.
But it was Burnley who got it, as Akinbiyi capitalised on indecision in the hosts' back-line to head home unmarked from six-yards.
The result was put beyond any doubt four minutes from time, as Cole swivelled on a six-pence before firing past Camp for his hat-trick.
QPR: Camp, Delaney, Mahon, Stewart, Buzsaky, Rowlands (Leigertwood 39), Connolly (Mancienne 90), Agyemang, Ephraim (Blackstock 69), Vine, Rehman.
Subs: Pickens, Lee.
Scorers: Mahon 14, Agyemang 30
Bookings: Leigertwood
Burnley: Jensen, Alexander, Harley, Caldwell, O'Connor (Spicer 90), Gudjonsson, Elliott, Lafferty, Blake (Akinbiyi 46), Varga, Cole (Randall 89).
Subs: Kiraly, Jordan.
Scorers: Cole 41, 55 & 86, Akinbiyi 77
Bookings: Varga
Referee: Mr K A Friend
Attendance: 13, 410
