The visitors were always the superior side in the routine result.
Fury goalkeeper Sebastian Usai struggled on debut, letting through Ruben Zadkovich's long range opener. Labinot Haliti pounced on a wayward Andre Kilian pass to double the lead in the 16th minute and Ryan Griffiths knocked in a third in the 70th minute.
Fury defender Mark Hughes scored from the spot late on to offer some consolation to home fans.
The two sides will now meet again at Energy Australia Stadium on Tuesday.