QPR chalked up their third win in four as Barnsley's miserable run stretched to nine outings without a win .
The Tykes - who have already avoided the drop - ended up firing blanks and 14-goal leading scorer Daniel Bogdanovic looks to have played his last game for the club.
The 30-year-old is out with a hamstring problem and is set to leave after next week's final game following the break down of talks over a new contract.
Neil Warnock's Rangers side were always the dominant force and should have been in front early on .
Rangers unbelievably missed the simplest of chances to go in front after 24 minutes. Dusko Tosic burst down the left, rounded Bobby Hassell and slipped slide rule pass for Antonio German.
German was perfectly placed about a yard out at the near post but the striker swung a casual effort with his left foot and it was blocked by his own right foot.
A minute later it was the turn of Radek Cerny to produce heroics at the other end when he blocked an Iain Hume effort then produced a super save to turn away Jon Macken's fierce follow up shot.
But after 27 minutes a bolt from the blue gave the visitors the lead. Leigertwood forged forward looking for options but then struck a sweet effort with his left foot from 25-yards that dipped over Steele and into the net for his fifth of the season.
Barnsley winger Adam Hammill whipped in a left flank cross that Macken headed but Cerny did well to stop and the Czech keeper made another top draw save when Hugo Colace beat the offside trap and smashed goalwards but he was equal to it.
Hammill was replaced by Martin Devaney before the break and the winger opened up a space on the left but dragged his low shot wide.
Colace should have done better early in the second half when Jacob Butterfield cut a neat low cross from the right but the Argentinian completely mishit his shot.