Leigertwood lashed home an excellent effort effort against the run of play midway through the first half to settle a drab encounter devoid of many good opportunities.
QPR goalkeeper Radek Cerny had to be alert to deny Iain Hume and Hugo Colace in the first half but the hosts struggled to break down the stubborn visitors and are now without a win in nine games, with QPR claiming their third win in four.
Barnsley boss Mark Robins made three changes to his side for their final home game of the season as Jon Macken, Bobby Hassell and Jacob Butterfield all came into the starting line-up.
Neil Warnock resisted the temptation to play some of his youngsters against Watford on Monday, but he gave young midfielder Josh Parker his first start today, with Tamas Priskin also coming into the side.
The Tykes made a good start and Hume found space on the edge of the box and got his shot away but Cerny did well to parry the ball away.
QPR responded and Akos Buszaky tried his luck with a free-kick from 30 yards but Luke Steele in the Barnsley goal was equal to the effort.
Hume then dragged a shot wide from 20 yards before Jonathan Macken saw an effort well blocked by Peter Ramage.
However, just as it looked like the Tykes might break the deadlock, QPR went ahead with 27 minutes gone.
Hogan Ephraim did well down the right and played the ball to Leigertwood who made no mistake with a fine finish into the top left-hand corner from just outside the box.
Barnsley responded well to going behind with Adam Hammill and Macken both having efforts saved by Cerny.
Colace, who was named Barnsley player of the year this week, also had a 20-yard shot parried away by the former Spurs stopper.
The Tykes suffered a further blow before the break when Hammill was forced off injured and QPR almost compounded their misery but Priskin volleyed over.
Both sides made a tentative start to the second-half and the first meaningful chance fell to Butterfield who failed to test Cerny with a shot from 25 yards.
Warnock brought striker Jay Simpson on for Antonio German in a bid to give his side more impetus up front but the on-loan Arsenal man struggled to get into the game.
Barnsley pressed forward in search of the equaliser but the visitors were proving a tough unit to break down, much to the frustration of the Oakwell crowd.
Hassell fired over from 25 yards late on but the home side were unable to find a way through.