The Roar won the shootout 6-5 with scores locked at 1-1 after 120 minutes, with back-up goalkeeper Jamie Young making the winning save to deny Jumpei Kusukami's sudden-death effort at Suncorp Stadium.
It was an easy save for Young, who was able to stay on his feet to pluck the spot-kick from the Japanese import to spark wild celebrations among the 17,530 fans in attendance.
Young was only on the field because first-choice stopper Michael Theo was forced off with a knee injury after a heavy collision with Terry Antonis in the first half of extra time.
It means the Roar are just one win away from a fourth A-League grand final appearance, if they beat Victory in their semi-final next week in Melbourne.
Thomas Broich, in possibly his final A-League appearance in Brisbane, played the entire match but did not take a penalty.
The Wanderers were reduced to 10 men in the 103rd minute when substitute Jaushua Sotirio was shown his second yellow card for clattering into Corey Brown - capping off a nightmare performance for the winger, who also spurned a golden chance to seal the win just before the end of regulation time.
The Wanderers were completely on top in the first half, dominating possession and territory and enjoying a glut of attacking chances on goal.
Only a couple of miracle efforts from Theo - who made a huge double save in the sixth minute to deny Brendon Santalab and Nico Martinez and then made a one-handed stop on 33 minutes to keep the Argentine at bay again - kept the home side in the match.
But Theo could do nothing about a controversial penalty converted by Antonis in first-half injury time, which put Western Sydney 1-0 up after Avraam Papadopoulos caught Brendon Santalab in the box with a late foot.
The Roar responded in the 55th minute through Jamie Maclaren, who tapped home into an empty net after Brandon Borrello's initial attempt came to him off the right post.
Both sides had their chances to win it in a frantic finish to regulation time - Borrello even managed to hit the crossbar twice with one shot in the 89th minute, which had first been parried by Vedran Janjetovic.