A last-gasp Jake Livermore winner capped a thrilling encounter on Albion's last visit to Loftus Road as the Baggies bagged all three points on the road.
Jefferson Montero netted after five minutes to hand the Baggies the advantage, but Luke Freeman levelled for the hosts before the break.
Jacob Murphy restored Albion's advantage just after the hour mark but Tomer Hemed converted a 75th-minute penalty to restore parity once more.
But, deep into injury time Mason Holgate found Livermore unmarked in the box, with the Baggies midfielder sweeping home from close range to spark celebratory scenes in front of Albion's travelling faithful.
Watch free-to-view highlights of the game above.