Chris Ramsey's men struck three times in the first half at the Hawthorns to leave Tony Pulis's men, who later had Youssouf Mulumbu, too far on the back foot to recover
Chris Ramsey's side have been dreadful on the road this season but Eduardo Vargas's superb goal midway through the first half set them on their way.
Charlie Austin scored a diving header before Bobby Zamora netted with a stunning chip as half-time loomed, putting Tony Pulis's men firmly on the back foot.
The Baggies responded throuh Victor Anichebe as QPR retreated into their own half after the break but the hosts could not force the issue - and they lost midfielder Youssouf Mulumbu to a straight red card after he raised his arm in a challenge with Joey Barton just before the end of normal time.
And Barton got the last laugh with a fourth away goal right before the final whistle.
West Brom had Brown Ideye back in the side after a knee problem and he sent a free header off target before Vargas put the visitors ahead in the 15th minute. The Chilean picked up the ball from Austin and, as the home defence backed off, he unleashed a 25-yard shot that flew into the bottom-left corner.
Ideye almost scored an equaliser four minutes later, although he knew little about it as Chris Baird's whipped cross struck his leg and flew wide of the right-hand post.
QPR suffered a blow on the half-hour mark when Vargas twisted his knee and had to be replaced by Niko Kranjcar, who soon had a telling impact in flicking on Matt Phillips's right-wing corner for Austin to nod home unmarked at the far post.
West Brom were stunned and, two minutes before the break, they fell further behind. Zamora ran onto Phillips's ball down the right channel and, from the corner of the box, lofted a superb finish with the outside of his left foot over Boaz Myhill and in off the crossbar.
The home faithful vented their frustration at half-time but their mood was improved 13 minutes into the second period when Anichebe rose to head in Saido Berahino's cross from the left. The Baggies' goalscorer was causing problems for the visiting defence and his knockdown fell to Ideye, whose strong drive was parried by Rob Green.
QPR felt that they should have had a penalty when Zamora's cross struck James Morrison's arm, before Ideye brought another save out of Green with a fierce volley from 20 yards.
Berahino ought to have further reduced the deficit 10 minutes from time but his free header from six yards was weak and comfortable for Green, before Ideye flicked Chris Brunt's cross narrowly over.
Mulumbu, on as a 72nd-minute substitute for Craig Gardner, was dismissed six minutes from time after leading with his arm in an aerial challenge with Barton, catching the QPR man in the face.
In the final minute of stoppage time, Barton completed the scoring with a left-footed drive following a scramble in the box as QPR ended a run of five consecutive defeats to move above Burnley into 18th in the table.