Curtin came from 2-0 down to win 4-3.
Rory Binnie kicked two goals, Nathan Smith got one and a late winner was the work of Eddie Tikoftruled.
The Balga scorers were Andrea Bouzinekis, Lee James and Medhi Rabeigholami.
Bouzinekis and James had Balga 2-0 up inside 20 minutes before a collision saw Curtin’s Albert Bucchino go to hospital with a broken nose. Curtin rallied from this point and struck back through a Binnie free kick in the 33rd minute.
After the break, it took only five minutes for Curtin to draw level through Binnie and took the lead as Smith scored yet another close range goal to give the visitors the lead on 65 minutes.
A corner resulted in Rabeigholami firing home to draw Balga level and it seemed that the scores would stay that way as the home team defended with grit.
But Curtin had one more trick up their sleeve – substitute Kristian Beven forced a turnover and Tikoft powered through the Balga defence and slotted past the advancing keeper.