Graham Arnold's entirely home-based squad showed glimpses of their potential as the game wore on and were denied a goal by one of their own with Sydney's Olyroos goalkeeper Tom Heward-Belle called into action on multiple occasions.
Sydney took the lead on five minutes from a corner that the Olyroos could not clear. Milos Ninkovic found the ball at his feet and he teed up Retre to stroke the ball home from 12 yards.
The lead was doubled on 15 minutes after a sweeping move that started down the left. Some neat interplay led to Rhyan Grant curling in a cross was clinically headed home from six yards by Buhagiar.
A misplaced pass out of defence by the Olyroos was pounced on by Buhagiar and he set up Baumjohann to fire past Tom Glover and make it three goals in 13 minutes for the Sky Blues.
It was a solid test for Sydney with coach Steve Corica now looking ahead to his team's meeting with Shanghai SIPG in Doha and then the new A-League season in late December.
"I think we were very clinical in that first 15-20 minutes, we played some very good stuff," Corica said. "We've got clearance to go to Qatar now.
"It's about mentally preparing, it's a good competition and good preparation for our A-League."
The game at Jubilee Stadium was watched by a small crowd and served as a final warm-up for Sydney before they fly out to Qatar on Saturday to complete their AFC Champions League campaign -- with their next group match on Nov. 19.
The Olyroos will face A-League newcomers Macarthur FC on Tuesday as they continue their preparations for next year's rescheduled Tokyo Olympics.