Kevin McLeod struck twice to end Luton's faint chances of a play-off place.
The on-loan Everton winger was left unmarked to head home a corner in the first half and his free-kick seven minutes from time bent around the defensive wall to leave the keeper stranded.
It was no more than QPR deserved. They dominated play throughout, were always first to the ball and left Luton chasing shadows for all but a five-minute spell in the second half.
The pattern of play was established as early as the second minute when Kevin Gallen was a toe end away from connecting to Richard Langley's low cross.
Seven minutes later Clarke Carlisle rose highest at a corner but sent his point blank header a yard over the bar.
Rangers piled on the pressure and Gallen's cross-shot beat the keeper, and also the outstretched foot of Paul Furlong diving in at the far post.
Luton's attacks were rare but Steve Howard stole up field in the 24th minute to warm the hands of Chris Day from 12 yards after the keeper could only half clear a cross.
It didn't take long for Mark Ovendale to be brought back into the action and the keeper's full length dive was equal to a flying header from Langley who was left unmarked in the box.
Yet another dangerous cross bisected the Hatters defence on 50 minutes and it was Gallen again who was a whisker from doubling the score.
Referee Joe Ross, who had had an indifferent game up until then, denied the home side a good claim for a penalty on the hour. Langley chased a loose ball in the box and fell under the challenge of Chris Coyne. Despite the vociferous appeals the referee waved away Rangers appeals.
Another lone Luton attack saw a jittery Day beaten to a centre by Adrian Forbes, but the smallest man on the pitch had to watch his header loop wide of the post.
When McLeod saw Ovendale marking the wrong side of the goal, he seized his chance and seconds after the ball nestled in the far corner of the net.
Hordes of Luton fans made their way to the exit aware that their season was over.