Down after Jackson Hart-Philips' 23-minute goal, South boss Sinisa Cohazdic turned to Juach at the break and the attacker delivered, striking in the 53rd, 60th, and 83rd minutes to propel Hellas to a famous win on Tuesday night.
It is the second time in as many years and third time overall a semi-professional National Premier League side has made the final.
South will meet Victory in an October 10 decider likely to be staged at AAMI Park, with the winner not only claiming silverware and a berth in next year's Asian Champions League 2, but bragging rights from the two teams' first competitive meeting.
Four-time champions of Australian football in the old National Soccer League, South were banished to the Victorian state leagues after the competition's 2004 collapse, with Victory serving as Melbourne's then lone side in the newly launched A-League the following year.
South's repeated attempts to re-join the Australian top-flight in the decades since have been rebuffed, with the club recently flagging their interest in taking up the licence left vacant by Western United's collapse.
"It's going to be one of the biggest games that we've seen in a number of years," skipper Marco Jankovic told AAP
"People have been waiting for it.
"And the timing now, with what's happening at the club, the changing of the guard, what we're doing in the OFC (Oceania Football Confederation) Pro League, our intention to go to the A-League, the timing - you couldn't really write it."
For much of the opening half, however, Lions FC looked like they were going to make their own run at history.
Representing Queensland's NPL in the semi-finals, the Lions took the lead when Hart-Philips met a Luke Broderick cutback and kissed an effort inside the far post.
Daniel Barber's side were also well-organised defensively and were a constant threat in transition, frustrating South.
But Juach's halftime introduction swung the game, the 25-year-old popping up in the six-yard box to turn in crosses from David Yoo and Hassan Ramazani to seize the lead, then adding a late sealer to send the 5,268 home fans into raptures.
"We recovered well," South midfielder Sebastian Pasquali told AAP.
"And that shows the togetherness of this group."
