Marc Nygaard grabbed a late goal as QPR twice came from behind to earn a point in a thriller at the Hawthorns.
West Brom led when Nathan Ellington scored from an acute angle after Jason Koumas' shot was saved and Diomansy Kamara made it 2-0 with a drilled shot.
Damion Stewart's far-post finish gave QPR hope on the stroke of half-time and Kevin Gallen turned in Dexter Blackstock's cross to level matters.
Kamara slid West Brom ahead before Nygaard netted from close-range.
West Brom manager Tony Mowbray:
"We dominated from start to finish and threw away two points. It was poor defending - you can't get away from it. If you score three at home you expect to win.
"We created plenty of chances which was pleasing but it's probably the first time I can say since I've come that we weren't solid at the back.
"I have felt very safe at the back over the last three or four weeks but I couldn't say that on this occasion."
QPR boss John Gregory:
"West Brom are the best side by a long, long way that I have seen in this division.
"You are almost looking at a Premiership side and quite frankly they should get automatic promotion with the team they have got. If they don't then they are selling everyone short. They were tremendous for the first 20-25 minutes.
"I feared the worst. I thought they should have killed us off but they didn't and to be fair that's a testament to the group of lads I've got. We are better than we played tonight, we gave away silly possession and gave away poor goals."
West Brom: Zuberbuhler, Watson, Perry, Curtis Davies, Albrechtsen, Gera, Greening, Wallwork (Hartson 86), Koumas, Ellington (Phillips 73), Kamara.
Subs Not Used: Hoult, Chaplow, McShane.
Goals: Ellington 8, Kamara 40, 54.
QPR: Royce, Mancienne, Rehman, Stewart, Bignot, Ainsworth, Lomas, Smith, Cook, Gallen, Blackstock (Nygaard 63).
Subs Not Used: Paul Jones, Milanese, Ward, Rowlands.
Booked: Smith, Bignot, Lomas.
Goals: Stewart 45, Gallen 48, Nygaard 83.
Ref: L Mason (Lancashire).