Former Sydney FC striker Marc Janko started for Austria and played 72 minutes for coach Marcel Koller's side.
But it was the midfield duo of Marko Arnautovic and Alessandro Schopf that gave Austria a healthy 2-0 lead inside 18 minutes.
While it looked bleak for Malta, they continued to fight and eventually got their reward in the 87th minute via Alaba's comical own goal.
Austria face Netherlands on Sunday morning (AEST) as they prepare for their opening EURO 2016 Group F fixture against Hungary on 15 June, before also facing Portugal and Iceland.