It was a straight forward victory for the Bhoys with Rogic providing an assist for Odsonne Edouard in the dying stages to secure the comprehensive win.
Mikael Lustig opened the scoring for Celtic on the cusp of halftime before Jozo Simunovic and Edouard added to the tally.
Rogic started the game and played the full 90 minutes with his assist in the dying stages wrapping up a solid performance.
The result means Celtic is on the cusp of claiming an incredible 'treble treble' with a clash against Hearts in the Scottish Cup final the only thing in their way.
Rogic is not the only Aussie set to take home silverware this season with shot stopper Danny Vukovic and his Belgian Club side KRC Genk closing in on the Belgium Pro League title.
Vukovic was unbeaten to claimed a clean sheet as Genk thrashed Roayl Antwerp 4-0 and stretch their lead at the top of the table to nine points ahead of second placed Club Brugge.
Vukovic's Socceroos teammate Apostolos Giannou found the back of the net for his Cypriot side AEK Larnacca overnight as they claimed a 1-1 draw against Nea Salamis.
Back in Scotland, former Socceroos striker Scott McDonald has helped Partick Thistle complete and incredible turn around as they secured saftey from relegation with a 3-0 win against Queen of the South on the last day of the league.
The Aussie front man found the back of the net in the win with a clinical finish in the 44th minute.
McDonald came out of retirement in February to help Thistle boss - and former Celtic teammate - Gary Caldwell going on to score seven goals and two assists from 13 games.
In Germany Matthew Leckie played 60 minutes for Hertha Berlin as they defeated Stuttgart 3-1 in the Bundesliga.
Robbie Kruse continued his exile from the Bochum first team as they claimed a 4-2 win in the German second division against 1.FC Magdeburg.
In Hong Kong Harry Sawyer secured championship success as his Tai Po side wrapped up the title with a 2-1 win against second placed R&F.
The 22-year-old former Newcastle Jets player was an unused substitute in the win.
