Joe Thomson's 25th-minute goal put Celtic in front before Kilmarnock equalised from a Paul Cairney penalty.
Socceroos star Rogic restored his team's advantage with a goal early in the second half, before Aidan Nesbitt doubled its lead with 15 minutes remaining on the clock.
Rory McKenzie's late strike for the home side meant little as Celtic consolidated second place with the win.
Of more interest to Socceroos fans was the eye-catching performance of Rogic, who tormented the Kilmarnock defence with a series of damaging runs into the penalty box.
Celtic's : "One purposeful burst from the Australian internationalist (sic) saw him tripped by Greg Kiltie, leading to the midfielder earning a stern telling off from the referee."
Rogic hasn't added to his five starts for Celtic's senior team since returning to the Scottish giant from a loan deal at Melbourne Victory in 2013/2014.
After playing 45 minutes on his return for the Hoops development team in its 2-0 win over Motherwell earlier this month, Rogic said: “At this point in my career I want to be playing first-team football, but after being out for so long I’m just very happy to get some minutes and I’m sure I’ll play a handful of games coming up for the development squad to get those important minutes in the legs after not playing for so long.
“Hopefully I can just help them and contribute to their season and progress as well in the short-term and look to build on that.
“There weren’t really any butterflies or anything and I’m not getting carried away as it was 45 minutes and the next step in my rehab.
“But it’s the first game situation I’ve had in a very long time and it’s just something I’m looking to build on.”
Rogic got 65 minutes to impress in the Kilmarnock game, pressing his claims for a spot in the first team with his goal icing another eye-catching display.