Kevin McLeod grabbed both goals as QPR made it three consecutive wins and consolidated their play-off position.
The on-loan winger from Everton struck once in each half to break the resistance of a physical Luton side in a scrappy game at Loftus Road.
QPR forced their way ahead six minutes before half-time.
Richard Langley swung over a corner from the left and winger McLeod rose highest to head the ball unchallenged into the net.
Paul Furlong and Kevin Gallen had both gone close in the first half and that continued after the break as first Gallen almost touched home McLeod's cross.
Furlong had an effort superbly saved and Langley was denied a penalty as he went for the rebound and appeared to be brought down.
Luton had their moments with Adrian Forbes forcing a great save from Chris Day and then heading inches wide from close range after Day had missed Kevin Nicholls' corner.
But Rangers had the cutting edge and made the points safe late on when McLeod let fly with a free-kick which had Mark Ovendale unsighted and found the bottom corner.
QPR: Day, Kelly, Carlisle, Shittu, Padula, Palmer, Bircham,
Langley, McLeod, Gallen, Furlong. Subs: Culkin, Rose, Pacquette,
Luton: Ovendale, Boyce, Coyne, Willmott, Davis, Spring,
Nicholls, Holmes, Hughes, Forbes, Howard. Subs: Beckwith,
Neilson, Bayliss, Jupp, Kimble.
Referee: J Ross (Essex)