Rangers were 2-0 down after 20 minutes when Joleon Lescott and Silvestre Varela struck for the visitors but Austin got the first of his three goals from the penalty spot just before half-time.
The striker then drew his side level early in the second period with a close-range finish before he lifted the roof at Loftus Road with a 87th-minute winner, heading home a Joey Barton corner.
Craig Gardner and Brown Ideye had both already fired presentable chances into the crowd before Lescott headed West Brom in front on 10 minutes.
The former Manchester City man was quickest to react to a near post Stephane Sessegnon flick following a Sebastien Pocognoli corner.
West Brom doubled their lead 10 minutes later when Varela’s clever one-two with Sessegnon cut open the QPR defence and the winger prodded home his first goal for the club.
With the Loftus Road crowd getting restless, QPR hit back with their first meaningful attack on 24 minutes.
Leroy Fer was adjudged to have been pulled back in the area by James Morrison as he threw himself at the ball after Ben Foster had spilled a Barton corner in his own six-yard box.
Austin stepped up and fired home from the spot, sending Foster the wrong way.
QPR continued on the front foot in the second period and were level on 48 minutes.
Richard Dunne rose highest from a Barton corner but could only divert his header against the crossbar. As the ball bobbled around the West Brom area, Bobby Zamora prodded the ball across the six-yard box and Austin was on hand to bundle the ball over the line from close range.
QPR had a penalty appeal waved away minutes later when Barton went flying in the box under a Morrison challenge as he went to latch onto an Austin knock-down.
Austin could have grabbed his hat-trick with 11 minutes remaining but was denied by Foster after substitute Junior Hoilett had dashed down the right and delivered a teasing cross.
But the match ball would be his for keeps just six minutes later as he completed the comeback for the hosts.
A superb Barton corner was met powerfully by the striker, who rose above Pocognoli to score his first Premier League hat-trick.
There was still time for West Brom substitute Saido Berahino to strike the crossbar in injury time as his side pushed Foster into the attack from a flurry of corners.
However, QPR stood firm and the win moves them out of the relegation zone – level on points with West Brom in 15th place.
Soccer Saturday verdict – Phil Thompson
“It wasn’t a game of high quality, but excitement was there all the time. There were chances at either end. West Brom started so fast and thoroughly deserved to be 2-0 up. The big thing for QPR is the home form and they were 2-0 down against a team that will be around them in the table. Would that demoralise them? It didn’t! They showed absolutely fantastic character to come back. Charlie Austin is a great story – it’s 11 Premier League goals for him now.”
QPR: Green (7), Onouha (6), Caulker (6), Dunne (6), Suk-Young (5), Vargas (7), Henry (6), Barton (7), Fer (6), Zamora (6), Austin (9).
Subs: Hill (7), Hoilett (7), Krancjar (6).
West Brom: Foster (6), Wisdom (6), Lescott (8), McAuley (6), Pocognoli (6), Gardner (7), Dorrans (7), Morrison (5), Varela (7), Sessegnon (8), Ideye (6).
Subs: Berahino (7), Gamboa (6).
Man of The Match: Charlie Austin