New Zealand international Chris Killen scored two goals in the space of three minutes late in the first half before substitute Koki Mizuno struck in the 50th minute with a brilliant diving header.
The hosts fought gamely to reduce the deficit but Roar keeper Liam Reddy continued to have a hard time of it with Celtic stand-in captain and Australia striker Scott McDonald influential before being replaced in the 61st minute.
Marc-Antoine Fortune, who recently completed a reported £3.8million move from Nancy to Glasgow, entered the fray at McDonald’s expense but failed to fire in his first appearance for the Hoops.
Fortune, like many Celtic players, appeared tired after the long flight, but still gave Celtic fans an exciting preview of his skills with a couple of deft touches.
The match, played in front of a boisterous crowd of 31,340 that featured plenty of Hoops supporters, was the first of four pre-season friendlies for Celtic in preparation for the opening UEFA Champions League qualifier.
The only sour note for the visitors was a possible knee injury to Milan Misun who looked to be in some pain after clashing with Roar midfielder Matt McKay.
The visitors started shakily and Polish keeper Artur Boruc was forced to produce a handful of saves to keep Brisbane youngster Robbie Kruse at bay in the opening stages.
Celtic took control of the contest and by the 20th minute, Reddy found himself under siege with Celtic trio Killen, McDonald and Shaun Maloney linking up smoothly in attack.
A sloppy touch from McDonald saw a goal go begging in the 32nd minute before Killen broke the deadlock in the 39th minute, nodding the ball home after a pinpoint cross from Lee Naylor.
Roar fans barely had time to catch their breath before Maloney released Killen, whose searing low strike from the edge of the penalty box found the back of Reddy’s net.
Killen was denied a chance at a hat-trick when Mowbray substituted the in-form striker at half-time, but the visitors continued to push and Mizuno claimed the best goal of the match when he threw himself at a great cross from Georgios Samaras.
The Roar’s annual Translink Cup encounter was marred by three pitch invaders who interrupted play in the second half.
Charlie Miller, one of three former Rangers players at the Roar, delivered a pre-match promise for a lively match with plenty of Old Firm rivalry and the playmaker did his best to inject some excitement late in the piece.
Miller was involved with some playful banter with the Celtic fans, but it was on the field where he made the biggest impact – getting the better of substitute keeper Lukasz Zaluska on three occasions but failing to find the net.