Akos Buzsaky was star man for the visitors with two terrific goals. He opened the scoring after 12 minutes, rifling a 25-yard effort beyond the reach of goalkeeper Joe Murphy.
Skipper Andy Crosby missed a great chance to equalise in the 22nd minute when he headed over from close range.
But two minutes later Scunthorpe were back on level terms when leading marksman Martin Paterson was on hand at the near post to tuck home an in-swinging corner from Kevan Hurst for his eighth goal of the season.
Hurst was then unlucky not to put the home side in front with a terrific strike from the edge of the box that crashed against the inside of a post and came out.
It was Buzsaky who struck again in the 42nd minute to put QPR back in front, when he curled a free-kick from the left-hand side of the box into the top far corner of the net.
With the driving wind and rain at their backs, Scunthorpe dominated the second half with a great save from Lee Camp denying midfield man Matt Sparrow in the opening minute.
Scunthorpe equalised in the 54th minute when a right-wing cross from Hurst deceived keeper Camp and came back off the far post for Jonathan Forte to force home the equaliser from close range.
In a rare second-half raid Buzsaky might have completed his hat-trick for QPR when he rifled over from 20 yards.
Scunthorpe pressed and pressed but could not find the winner they searched so desperately for late on.