Goals from Gary Hooper and Charlie Mulgrew handed Celtic their first pre-season victory but it came as a cost with influential midfielder Beram Kayal going off injured with a facial knock.
Kayal suffered a heavy blow to his nose and left the field after failing to stem the flow of blood.
Hooper had earlier given Celtic the lead with a composed finish and Mulgrew made it 2-0 with a header early in the second period.
Neil Lennon's men won comfortably against a team managed by former Rangers midfielder Ian Ferguson, who included ex-Celtic player Liam Miller in his starting line-up.
Mulgrew and Kris Commons came into the Celtic team after missing last weekend's 1-0 defeat by Central Coast Mariners because of muscle fatigue, but there was still no place for Thomas Rogne, who had been left out for the same reason.
Kelvin Wilson and Glenn Loovens continued in central defence with Lukasz Zaluska behind them and Mark Wilson and Mulgrew at full-back. Scott Brown started on the right of midfield with Commons the other side of Kayal and Joe Ledley.
Celtic began brightly, forcing a series of corners, and took the lead in the 16th minute.
Anthony Stokes let go a hopeful long ball from Loovens and the home defence failed to match Hooper's inside run, leaving the striker free to bear down on goal before slipping the ball past Danny Vukovic and inside the post.
Commons saw a 30-yard free-kick deflected just wide before Miller set up Perth's first chance with a clever free-kick to the back post. Shane Smeltz ran clear of Commons but fluffed his attempted volley.
Miller, who left Hibernian in May, soon fired just over after some good skill on the edge of the box.
The game was then held up for four minutes as Kayal received treatment after being unintentionally caught by the elbow of Adam Hughes during an aerial challenge. The Israel international could not continue and Shaun Maloney came on in the 34th minute.
The game entered a scrappy phase before Celtic had a decent penalty claim denied in injury-time when Stokes appeared to be pushed over after weaving in between two Glory players.
Cha Du-ri and Ki Sung-yueng came on at half-time for Mark Wilson and Commons, while the home side introduced former Motherwell midfielder Steven McGarry.
Lukasz Zaluska, who looked assured throughout, made his best save of the game 90 seconds into the half when he pushed away a 25-yard strike from Hughes after Cha's loose pass.
Celtic immediately responded with Maloney's low cross finding Stokes eight yards out, but the striker's shot was well blocked.
The Hoops doubled their lead in the 51st minute when Mulgrew rose well eight yards out to head Ki's inswinging free-kick into the corner of the net.
Celtic were in complete control for the rest of the game with Paddy McCourt, Daryl Murphy and Adam Matthews all given run-outs. McCourt saw a lot of the ball and threatened to get in behind the hosts on several occasions but Celtic, who finish their Australian tour against Melbourne Victory on Wednesday, were content with their lead.