The Loftus Road side have spent £5million on eight signings since Indian multi-billionaire Lakshmi Mittal bought a stake in the side.
Rangers, who were propping up the Championship earlier in the season, had snatched the lead against a United side with just one win from their last seven games, before they were hit with two goals in a four-minute spell.
Akos Buzsaky, one of eight new signings in the transfer window, almost found a way through early in the game, but his low strike was saved by the diving Paddy Kenny.
Dangerman Buzsaky, snapped up from Plymouth for £500,000, was then foiled by Kenny who tipped his stinging free-kick over the bar in spectacular fashion before United woke up.
Keeper Lee Camp pulled off two vital stops, pushing David Carney's strike around the post and palming away Rob Hulse's deceptive cross.
Rangers went ahead seconds before the break when Leigh Bromby failed to clear Matthew Connolly's cross from the right as Patrick Agyemang lashed the ball into the roof of the net from six yards.
Billy Sharp almost set up an equaliser from the restart, as he chased into the area to lob the ball over Camp's head, but Fitz Hall stuck out a foot to clear and the ball fell to Hulse who headed wide from close range.
United were back on level terms in bizarre fashion in the 64th minute. Michael Tonge's long-range strike was pushed away by Camp but, when Martin Rowlands tried to clear, he lashed the ball against Damion Stewart and it spun over the line.
Hendrie grabbed the winner in the 68th minute after he and Connolly challenged for Billy Sharp's cross. The little midfielder was first to his feet as he swept the ball into the net from six yards.
United centre-back Matt Kilgallon pulled off a stunning clearance seconds from time jumping to clear Martin Rowlands' long-range strike off the line.