ahead on the night - and drew level on aggregate - when Bridge broke his goal-scoring drought with a sublime finish on 53 minutes.
Byun's cross was met by Kisel at the back post and the Slovak showed great presence of mind to lay the ball back to Bridge on the edge of the box.
The No.19 produced a lovely first touch to shrug off Grant Brebner and hit a sweet left-foot shot past Langerak for his first goal since Round 13.
Chances continued to fall at both ends, Brebner blasting an attempt deep into the Melbourne faithful behind the Sydney goal after two delightful back heels opened up a chance after 74 minutes.
Byun again tried his luck from distance, turning away in despair as his volley strayed just left of the post minutes later.
Thompson, back from injury and brought into the game after 65 minutes, could have buried Sydney late in regular time.
But after finding himself one-on-one with the keeper, the Victory striker showed signs of rustiness in hitting his shot directly at the advancing Bolton.
But there was to be no late goal, the match going to extra time.
The Victory enjoyed the best of what was on offer early, Bolton twice saving from point-blank range as first Marvin Angulo and then Hernandez took aim.
But it was Thompson - courtesy of some quick thinking from crowd villain Muscat - who decided it with an opportunist's goal seven minutes before the end of extra time.
Sydney FC 2 (Kisel 36p, Bridge 53)
Melbourne 2 (Kruse 15, Thompson 113)