James McOwen scored the game-winning run by coming home on a wild pitch in the bottom of the 13th to give the Heat a 7-6 victory over the Jet Couriers Melbourne Aces.
The game can been seen at noon ET on Sunday on MLB Network.
Virgil Vasquez, who earned the victory in Game 1, was named series MVP.
Mychal Givens led Perth with four hits, while Allan de San Miguel and Mathew Kennelly each knocked two. Jose Davies went 4-for-6 to lead Melbourne.
Each team scored three times in the opening inning and Melbourne later took the lead by keeping up the early fireworks, leading, 6-3, after three innings. Perth came back quickly, scoring once in the fourth and twice in the fifth.
The game remained tied until the 13th inning, when McOwen led off by getting hit by a pitch and then was sacrificed to second and moved to third on a ground out. With two outs, Melbourne's Andrew Russell threw the second pitch to Corey Adamson wildly, bringing McOwen home and ending the game.
A record nine Australians played in the Majors last season, and about 70 more in the Minor Leagues, with some of them participating in this ABL postseason. Paul Archey, MLB senior vice president of international business operations, said this ABL season has been indicative of the sport's rising popularity in Australia and a growing stream of talent.
"Australia has been a growing market for us over the last 20 years," Archey said during the last round. "We saw a lot of development take place because of the old Australian Baseball League -- players choosing baseball because it had a profile, and this was a market where we thought we could start the ABL back. Not just for the fans, but for development as well.
"We're seeing great talent at the youth level, and you'll continue to see Australia in the Major Leagues, that's for sure."