Austin - the top English scorer in the division - headed home the winning goal in the 87th minute to complete a stunning comeback for Harry Redknapp's side - who move out of the bottom three.
Joleon Lescott and Silvestre Varela each struck their first goals for Albion as the visitors raced into a dominant lead inside the opening 20 minutes.
Austin pulled a goal back for Harry Redknapp's side before the break with an emphatic penalty, and he levelled the scores with a neat finish early in the second half.
And with time running out, Austin made no mistake from Joey Barton's corner to take his tally for the season to 11 - bettered only by Diego Costa and Sergio Aguero.
Victory moves QPR out of the relegation zone at the expense of Burnley - who lost 2-1 at Tottenham - and level on 17 points with 14th-placed Albion.
The visitors, who named an unchanged side, started brightly and wasted two chances in the opening seven minutes as Rob Green saved from Craig Gardner and Brown Ideye fired over.
West Brom's early pressure finally paid dividends after 10 minutes as Lescott headed beyond Green from Sebastian Pocognoli's corner, the central defender beating Richard Dunne to a Stephane Sessegnon flick-on to score.
QPR's attempts to get back into the game failed to produce anything to test Ben Foster, and after 20 minutes West Brom delivered a sucker-punch with a second goal on the counter-attack.
Eduardo Vargas needlessly gave away possession in the West Brom half and Varela raced towards the QPR penalty area before executing a neat one-two with Sessegnon and poking the ball under Green.
Four minutes later the hosts were handed a way back into the game as Leroy Fer was dragged back by James Morrison in the penalty area, after Foster had failed to claim a corner.
Austin - returning from suspension as one of four QPR changes - stepped up and lashed a powerful shot down the middle from 12 yards.
The striker could have doubled his tally before half-time, but he saw an effort saved by Foster and then fired over from 18 yards.
QPR's growing momentum continued at the start of the second half and three minutes after the break they were level through Austin.
After Dunne saw a header crash against the crossbar, Bobby Zamora reacted quickly to find his strike partner, and the 25-year-old applied the finish.
Having overcome the shock of throwing away their advantage the visitors worked their way back into the game, however their final pass was notably lacking.
And that slackness was punished with three minutes of normal time to go as Austin thudded Barton's right-wing delivery home to complete his treble and ensure a happier Christmas for QPR fans and staff alike.
