Rogic side-footed a classy finish in the 46th minute to make it 2-0 in the League Cup match.
It was the 26-year-old's first start for the Hoops since May last year after recovering from a knee injury.
Celtic coach Neil Lennon was full of praise for the Socceroos midfielder after the match.
"Tom Rogic was brilliant. He’s got the bit between his teeth and he looks night and day compared to how he was last season," Lennon says.
Rogic has been at Celtic since 2013, playing 170 matches in that time and scoring 36 goals.
Celtic next play Hibernian on Saturday night (AEST).
