Top-scorer Charlie Austin's strike and a Jean-Yves M'voto own goal gave the away side a half-time lead, while a brilliant solo effort from Yun Suk-Young capped the victory after the break.
Barnsley fought hard, and scored twice through Chris O'Grady, but too often did not have the quality to go with their work-rate.
Both teams made a host of changes. With most of Barnsley's loan players returning this week the hosts made five, while QPR fielded seven changes with one eye on their upcoming play-off campaign.
Kevin Doyle was first to try his luck for the visitors, the striker on loan from Wolves cut in from the left but fired his shot wide of Luke Steele's goal.
Barnsley did the majority of the early pushing however, and after a succession of corners Dale Jennings hit the side-netting when played through by player-of-the-season O'Grady.
Midway through the half QPR's experienced players were showing their composure on the ball, but the match had a distinct end-of-season flatness about it.
Jennings went close again for the hosts, his free-kick finding the arms of visiting goalkeeper Rob Green.
Things were livened up when QPR grabbed the lead in the 42nd minute. Charlie Austin found space in the box, received the ball and with time to compose himself neatly finished.
Within moments the visitors' lead was doubled by an own goal. Doyle's dipping cross from the right caused uncertainty and Barnsley defender Jean-Yves M'voto's intervention could only slice the ball over his keeper and into the net, giving QPR a two-goal cushion at half-time.
Not long after the start of the second period young Barnsley striker Danny Rose saw a goalbound volley blocked by QPR captain Nedum Onuoha.
O'Grady then put a shot wide for the hosts, who were showing fight and clearly keen to get themselves back into the game.
With the game more open, Armand Traore fired in a powerful 25-yard shot that was well saved by Steele in the Barnsley goal.
On 54 minutes the home side did get a goal back, Jennings' left-wing cross found O'Grady eight yards out and the striker's low header hit the target for his 14th goal of the season.
However, chances of a home fightback were all but extinguished in the 68th minute when full back Yun scored a scintillating solo goal. The South Korean sped past three Barnsley defenders then finished emphatically to restore his side's two-goal lead.
Onuoha headed narrowly wide from a set piece with the visitors looking comfortable in their lead.
As the game crept into injury time O'Grady gave Barnsley hope with a curling effort from 25 yards, but it was too late for the hosts, who went out of the Championship on the back of a defeat.
QPR will hope to exit the division from the other end later this month, but will face sterner tests if they are to be successful in the play-offs.