Goals to Nathan Smith and Bryce Young were enough to get the job done for the university team.
Young and fellow full- back Chase Parker were solid for Curtin and were able to keep Fremantle at bay for long stretches of the game.
Midway through the first half some intricate play between Carlo Chiellini, Kristian Beven and Rory Binnie set up Smith, who buried the ball in the bottom corner from 15m.
Minutes later Beven found some space at the edge of the box, but his shot sailed wide.
With five minutes left in the half, Smith drove a shot that left Fremantle keeper Peter Wile stranded, but it sailed wide and the teams went into the break at 1-0.
Fremantle started strongly in the second half and capitalised from a corner when Andrew Morrow’s towering header found the back of the net.
Curtin keeper Calum McMulkin came to the rescue on 70 minutes when he saved at point blank range to keep the teams level.
With only minutes to go, Chiellini set up a shot for Jon Krawec, who forced a fine save from Wile, only for the ball to fall to Young’s feet and he tapped home for the visitors to snatch victory.
Curtin plays Ellenbrook United on Friday night in what is sure to be an entertaining clash of the league’s newest teams.