A second-half goal from substitute Scott Brown was enough to give Neil Lennon’s side their second victory Down Under.
A 1-0 defeat by Central Coast Mariner in Celtic’s opening game was followed up by a 2-0 success over Perth Glory.
The Parkhead club, skippered by their Greece striker Georgios Samaras as a tribute to the big Greek community in the city, were worthy of their win in what was another highly-competitive friendly match.
And had it not been for home goalkeeper Tando Velaphi, the margin of victory for Lennon’s side would have been greater.
In front of a crowd of 20,794, many of whom were backing the Glasgow club, the 24-year-old pulled off a string of fine saves to thwart the Hoops, only to be beaten by Brown’s 78th-minute drive.
He twice denied Samaras in the first half and his save from Charlie Mulgrew’s free-kick just after the break, when he tipped the ball over the bar, was particularly impressive.
Samaras then slipped in Paddy McCourt on the left and the Irishman skipped past one defender before his low shot from an angle was turned away by the Melbourne keeper.
That let-off seemed to spark the home side into action again.
Daniel Allsopp passed up two decent chances, including a near-post header with which he should have opened the scoring.
He did better shortly after in setting up Archie Thompson with a perfectly-weighted through ball but he screwed his shot wide for a throw-in.
Celtic responded positively again with Kris Commons picking out McCourt at the far post with a wonderful delivery but the former Derry City player was unable to keep his header down.
Lennon’s side dominated the closing stages. Striker Gary Hooper’s low cross was almost turned into his own net by Adrian Leijer, before Anthony Stokes – on for McCourt – drove into the side-netting.
Hooper was then unable to get on to the end of Samaras’ inviting pass which would have surely resulted in a goal had he connected.
However, with 12 minutes remaining the Parkhead men were rewarded for their efforts.
Commons took a quick corner and found Brown, on for Beram Kayal, at the edge of the area and his shot took a slight deflection before finding its way in to the corner of the net.
There was still time for Stokes to hit the bar with a free-kick, while Daryl Murphy, who had replaced Hooper, also came close on two occasions before the final whistle.