Sean Dyche’s side arrived at Loftus Road on Saturday looking to extend a four-match unbeaten run, but they found Robert Green in inspired form in the opening half and failed to breach a well-marshalled home defence after the break.
Austin was sent off for a second bookable offence moments after doubling the lead for the hosts, but Burnley could not make their numerical advantage count over the final 20 minutes.
The outcome could have been vastly different had Burnley converted some clear-cut openings in an entertaining first 45 minutes, but a combination of Green and the woodwork kept the scoreline goalless.
After Ashley Barnes had sliced wide from the edge of the box, Scott Arfield appeared set to break the deadlock when Green collided with Mauricio Isla as he attempted to claim a cross.
But Green picked upself up to block Arfield’s shot with his face and Richard Dunne was on hand to mop up and clear the danger.
Both teams looked to get forward at every opportunity, but they were let down by the final ball when getting into a threatening position.
However, Green then pulled off one of the saves of the season to deny George Boyd after the home side had failed to fully clear a Burnley corner on the half-hour mark.
Boyd’s well-struck 25-yarder looked destined for the top corner, but Green flung himself to his left and got just enough glove on the ball to deflect it onto the post.
QPR then responded with a flowing move that resulted in a huge chance for Eduardo Vargas, who cut in from the left and beat Tom Heaton only to have his shot blocked on the goalline by Michael Keane.
Jason Shackell threw himself in front of a decent shot from Fer as QPR began to get on top, and Shackell then did well to deny Austin a shooting chance seconds before the interval.
Shackell was again well-placed to divert another Vargas effort behind before QPR’s bright start to the second half was rewarded with the opening goal on 50 minutes.
Bobby Zamora’s delightful flick released Austin and the former Burnley striker squared for Fer, whose shot took a huge deflection off the sliding Ben Mee and ballooned over Heaton and into the net.
Burnley responded in positive style, but Danny Ings headed wastefully wide at the far post before Boyd blazed over the bar and Heaton got down well to his right to keep out Joey Barton’s low fizzer at the other end.
But Heaton was powerless to prevent QPR’s second goal in the 73rd minute as Isla picked up a superb crossfield pass from Niko Kranjcar and squared for Austin to power home from six yards.
Austin had been booked a minute before scoring, and he received his marching orders moments afterwards after appearing to catch Keane in the face with a loose arm as they contested a header.
Boyd escaped a yellow card for a similar challenge on Dunne, who got his head to a number of balls into the box as Burnley opted for route one in the closing 10 minutes.
But it was QPR who came closest to scoring again when Barton latched onto a precision pass from Fer before having his shot beaten away by Heaton.
Green’s goal was rarely under threat over the final five minutes, and Hull’s goalless draw at home to West Brom allowed Harry Redknapp’s side to move a point clear of the drop zone.
QPR: Green (8), Isla (7), Caulker (7), Dunne (8), Yun (6), Vargas (6), Barton (7), Henry (6), Fer (8), Austin (7), Zamora (7).
Subs used: Kranjcar (7), Mutch (5), Phillips (5)
Burnley: Heaton (6), Trippier (5), Keane (6), Shackell (7), Mee (6), Boyd (7), Marney (5), Jones (5), Arfield (6), Barnes (6), Ings (6).
Subs used: Wallace (5), Jutkiewicz (5), Sordell (5).
Man of the match: Leroy Fer.