© Getty Images
© Getty Images
Perch tried to set up a second goal later in the first half, but Shaun Maloney could not squeeze the ball in from his cross.
QPR were on the attack early in the second half as they tried to get back on level terms, but a curling effort from Junior Hoilett crept just wide.
Just five minutes later, the Hoops were awarded a spot kick of their own down the other end when a mistimed challenge from Gary Caldwell brought down Hoilett, allowing Charlie Austin to level from the spot.
Wigan brought Martyn Waghorn off the bench in a bid to restore their lead, but his first shot of the night went straight into the hands of Robert Green.
Carson was kept busy in the closing minutes of the regulation 90 minutes, with Bobby Zamora looking for the winner for QPR, but the Wigan keeper did enough to send the game into extra time.
QPR took the lead for the first time in the two legs of this tie just six minutes into the additional period when Zamora played the ball in for Austin, who quickly unleashed a powerful strike to claim his second of the day.
The striker had a chance to wrap up his hat-trick at the start of the second half of extra time as he tried to volley the ball in from outside the box, but Carson was able to tip the ball over.
Wigan piled forward in the final minutes of the match as they desperately sought an equaliser, but could not find the back of the net.
QPR will face Derby County in the final at Wembley for a place in the Premier League later this month.