Olympic booked their place in the next round through a final-play win in extra time.

The home side were restricted to 10 men for the last 30 minutes but substitute Jeremy Habtemariam defied the mismatch and lifted his club to the finest moment in its 60-year history.

In the initial stages, Olympic struggled to take possession of the ball, which made it difficult to leave their defensive half.

But the home side's back four were well structured and easily contained Green Gully, who, despite dominating territory and possession, were sloppy in front of goal.

Tim Bobolas struck a missile at goal that excited the local crowd but was controlled by Gully's goalkeeper, Sebastian Mattei.

But the best chance of the half belonged to Gully's Liam Boland, who curved a free kick into the corner of the goals, which was tipped out by a scrambling Angelo Konstantinou.

By half time, the nil-all scoreline flattered Olympic, with Gully failing to put away up to three clear chances at goal.

Olympic began the second half more positively until a fiery passage of play and then an illegal tackle straight afterwards led to the second yellow card to Adam Rogic in the 60th minute.

With one fewer player on the field, scoring opportunities became more frequent.

Olympic coach Frank Cachia brought lively Habtemariam onto the pitch and the side immediately looked ominous in front of goal.

Green Gully tired and failed to capitalise on their extra-player advantage, and Habtemariam's pressure eventually led to a penalty in the final minute of extra time.

Goalkeeper Konstantinou then calmly strolled down the pitch and put away the penalty, and so continued Olympic's remarkable season.

When Olympic qualified for the FFA Cup earlier this year, Cachia said he wanted to play an A-League side. He'll now get his wish.

"I'm sure people will point to the fact we haven't played an A-League side as yet, but we've actually beaten two teams who have beaten A-League sides and we've done it without conceding a goal," Cachia said.

He said he sweated over the decision to play Habtemariam off the bench but it was his energy when he came on that changed the game.

"Jeremy was the hardest decision I had to make all year, whether I started him or not," he said.

"I made the call early in the week that I would start him off the bench because, out of all the players in that squad, he's had the most impact off the bench.

"I pulled him to the side on Sunday when we trained and I told him the news he would start on the bench, but I told him 'you will win it for us, you will win us this game'."

The other semi-final will be a derby between Melbourne Victory and Melbourne City.

FFA CUP QUARTER-FINAL

Canberra Olympic 1 (Angelo Konstantinou 95' pen) def Green Gully 0