A comical error from the goalkeeper gifted the Baggies a two-goal lead after Chris Brunt's opener that the hosts could only halve thanks to Djibril Cisse's intelligent finish
A first-half strike from Chris Brunt and a Robert Green own goal gave the visitors a convincing lead - one that they would hold onto despite a Djibril Cisse goal that briefly inspired the home side.
The hosts began the game positively as Stephane Mbia curled a shot from 20 yards just wide of Ben Foster's post but that turned out to be the only moment of danger either side posed until the 24th minute.
Shaun Wright-Phillips injected the pace and trickery that QPR fans had rarely seen from the winger as he escaped the attentions of Marc-Antoine Fortune and Billy Jones before lifting a precise cross to Jamie Mackie, who could only head wide of the far post.
West Brom had barely threatened Green's goal to this point, but the excellent Youssuf Mulumbu, reinstated to the side following suspension, was afforded too much time in the hosts' half, allowing him to feed the ball into Brunt. The Northern Irishman had ample space to steady himself and rifle a powerful low drive from 25 yards past Green to hand the visitors the lead.
Moments later James Morrison volleyed just over Green's crossbar, before QPR began to reassert themselves. Mbia saw Foster turn his shot from range around the post, before the former England goalkeeper leapt nervously to his right as Adel Taarabt's free-kick whistled just wide of his post.
Though Clint Hill nodded a corner wide, Steve Clarke's side finished strongly as both Zoltan Gera and Morrison curled efforts the wrong side of Green's post.
West Brom carried their momentum into the second period and although Anton Ferdinand was fortunate to see his chested clearance rebound behind the goal and not past Green, the Rs were not as fortunate moments later.
Armand Traore's skyward header from Brunt's corner caused consternation in the box, allowing Fortune the time to back into Green on the goal line. As the two players jostled, it was Green's touch as he tried to palm the ball over his bar that saw QPR fall 2-0 down. The hosts felt aggrieved but referee Chris Foy adjudged the tangle to be legal.
From there West Brom were unlucky not to net a third as Morrison laid Romelu Lukaku in on goal, but the giant Belgian saw his finish well saved by Green.
As QPR chased the game Redknapp introduced Junior Hoilett and Samba Diakite and although Lukaku trundled through on goal only to be denied by Green once more, it injected new life into QPR.
Mbia, who had been one of the hosts' better players, found room to slide a ball into Cisse. With the pace just right, the Frenchman did not need to break stride as he lifted his finish over the onrushing Foster to provide QPR with some hope.
Though QPR grew in confidence, the Baggies remained resolute, though they had to rely on a superb save from Foster in the dying stages to prevent Hill's header equalising. Clarke's team rode their luck as they clung onto their lead, especially as Liam Ridgewell handled Mbia's back post header, much to the fury of the Cameroon midfielder.
A seige on the West Brom goal yielded plenty of half-chances but by the final whistle the Midlands side survived, preserving their place in the Premier League's top six.