Nathan Smith and Khaled Salhah had Curtin on their way early, but it was a goal to defender Chase Parker in the dying minutes that got Curtin all three points.
Inside 15 minutes, Curtin had jumped to a two-goal lead.
Smith broke clear with pace and finished low into the bottom corner and then Salhah finished smartly at the far post.
It was just before the break that Quinns got back into the game with a sweeping move finished off by Sam Doherty. The teams went into the half time break with Curtin leading their hosts 2-1.
It took Quinns seven minutes of the second half for Smith to level the scores. A challenge then left Curtin’s Smith unable to continue because of injury.
This sparked Curtin into action and Parker found the winner with five minutes left to play.