Chris Brunt's fine first-half strike put the Baggies in front before a contentious second, which saw Robert Green fumble the ball into his own net, doubled their lead.
Djibril Cisse pulled one back for the hosts, who threw everything forward in the closing stages, but there was to be no festive cheer for the locals who made it to Loftus Road for a fixture which started late due to travel disruption in the capital.
QPR looked the more likely of the two sides to score early on, but it was the Baggies fans who were celebrating just before the half hour when Brunt put the visitors ahead.
The midfielder picked the ball up from Marc-Antoine Fortune and, after allowing it to drift across his body, unleashed a 25-yard drive that sailed into the bottom right-hand corner of Green's goal.
James Morrison almost made it 2-0 seconds later with a clever volley, but the home side regained their composure and went close through Stephane Mbia and Adel Taarabt.
After the break the story remained the same. Romelu Lukaku found space in the box, but could only prod weakly at Green and Anton Ferdinand almost turned Billy Jones' cross in to his own net.
Mbia summed up the lack of quality in front of goal for QPR when he wriggled free from his marker to meet Taarabt's corner, but his header flew straight back at the Moroccan, rather than at goal.
The home fans were then outraged as West Brom doubled their lead in controversial circumstances on 49 minutes.
Traore attempted to clear Brunt's corner but instead his header looped back towards his own goal. Green attempted to collect the ball but he was impeded by Fortune, who leaned in to the stopper, causing him to drop the ball into his own net.
The away fans ironically chanted Green's name as the Rangers players demanded Fortune be penalised for the foul, but referee Chris Foy shook his head and the goal stood.
Albion took their foot off the accelerator after that and paid the price in the 69th minute when Cisse latched on to Mbia's slide-rule pass and lifted the ball over the advancing Ben Foster.
QPR threw everything at the away goal looking for an equaliser, but they struggled to test Foster.