Managerless QPR were well beaten by the Championship leaders.
Johann Berg Gudmundsson opened the scoring in the 19th minute and on-loan Chelsea left-back Ian Maatsen doubled the Clarets’ lead in first-half stoppage time.
And Nathan Tella’s 71st-minute goal, after a mistake by Jimmy Dunne, sealed a resounding victory for Burnley and added to their opponents’ woes in the wake of Mick Beale’s departure.
Gudmundsson, restored to the side by boss Vincent Kompany, vindicated his inclusion by scoring in fine style, sweeping a left-footed free-kick into the far corner of the net beyond keeper Seny Dieng, who barely moved.
QPR had some reason to feel aggrieved about the free-kick for a foul on Jack Cork, who went down after very little contact near the edge of the penalty area.
The hosts also had strong appeals for a penalty in the opening minute waved away when George Thomas went down under a challenge from Arijanet Muric.
From the following goal-kick by keeper Muric, Rangers switched off and Tella found himself in on goal, but the on-loan Southampton midfielder shot tamely at Dieng.
After Gudmundsson’s opener, Chris Willock missed a glorious chance to equalise when he blasted over after being set up by Ethan Laird.
Apart from that scare, though, Burnley looked comfortable – and a second goal just before the interval was a hammer blow for QPR.
Senegal international Dieng, just back from the World Cup, dived to his right to keep out Vitinho’s strike only for Maatsen, lurking on the left-hand side of the penalty area, to follow up with an emphatic first-time finish.
Paul Hall, placed in interim charge following Beale’s recent decision to swap west London for Glasgow and the Rangers manager’s job, made a double change at half-time, sending on Albert Adomah and Olamide Shodipo in place of George Thomas and the out-of-sorts Willock.
QPR did rally in the second half and an effort from Sam Field was well saved by Muric.
However, their hopes of a comeback were crushed by Tella’s seventh goal of the season.
Former Burnley defender Dunne made an unwise decision to try to chest the ball back to Dieng, and Tella nipped in to score from what seemed an impossible angle.
The defeat was QPR’s fourth in a row and fifth in their past six matches – a run which has seen them slide from top of the table to ninth.
QPR (4-3-2-1): Dieng; Laird, Dunne, Clarke-Salter, Paal; Field, Iroegbunam, Dozzell (Armstrong 76); Willock (Adomah 45), Thomas (Shodipo 45); Dykes.
Subs not used: Archer, Kakay, Dickie, Richards.