Big-spending QPR, who won 2-1 on aggregate after a 0-0 draw at Wigan in the first leg, must now beat Derby County in the Wembley final on May 24 to make an immediate return to the Premier League.
James Perch turned in a cross from close range to put last season's FA Cup winners Wigan ahead early on but QPR top scorer Austin equalised with a 73rd-minute penalty after Gary Caldwell's rash challenge on Junior Hoilett on the edge of the box.
With their Loftus Road home bouncing to a constant roar from an expectant crowd, Austin then took advantage of some lax defending to prod home Bobby Zamora's dinked pass six minutes into extra time.
Malaysian-owned QPR were favourites to go up automatically but lost out to Leicester City and Burnley, finishing fourth behind third-placed Derby, managed by ex-England boss and Harry Redknapp's former QPR assistant Steve McClaren.
Wigan, who were also hoping to bounce straight back into the world's richest domestic league, could have gone 2-0 in front had James McClean not hit the post minutes before Austin's first goal.
Derby's 6-2 aggregate success over Brighton & Hove Albion on Sunday led to beaten Spanish manager Oscar Garcia resigning on Monday.
(Writing by Mark Meadows; editing by Ken Ferris)
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