Rogic, whose time at Celtic has been plagued by injury and interrupted by a loan spell at Melbourne Victory, marked his first start for the Hoops in nearly two years with a fine flicked finish with his heel to open the scoring in the 28th minute.
Kris Commons then showed good awareness to take advantage of a lapse of concentration in the Thistle defence by chipping in Celtic's second in the 63rd minute, sealing a 14th consecutive win over their Glasgow rivals.
"I think the first 35 minutes was some of the best football we've played this season," said Celtic manager Ronny Deila.
"But we got a little bit tired at the end of the second half and we were a little bit sloppy."
The win means Celtic now occupy their familiar position at the top of the league table ahead of newly promoted Hearts -- who defeated Dundee 2-1 on Saturday -- on goal difference.
Thistle manager Alan Archibald admitted that his side had not done enough in the game.
"We didn't pressure Celtic enough and they probably played in second or third gear for long spells of the game, which was disappointing," Archibald said. "I know that we are a lot better than that."
Celtic made three changes from their mid-week Champions League qualifier against Qarabag, with Rogic, Commons and Leigh Griffiths coming in for the injured Scott Brown, Gary Mackay-Steven and the suspended Nadir Ciftci.
The Scottish champions showed no signs of a European hangover, with Griffiths quick to test the Thistle defence as he rose at the back post to narrowly direct a header over from an Emilio Izaguirre cross.
- Debut for Pogba -
Celtic then laid siege to the Thistle goal, with Tomas Cerny making a save from Commons's low drive before holding Griffiths's dipping free-kick.
The Thistle shot-stopper was doing his best to keep his side on level terms as he made a point-blank save to deny Griffiths before a rasping 30-yard strike from Virgil van Dijk cracked against the base of the post.
A goal was coming and it came from the unlikely source of Rogic in the 28th minute.
Callum McGregor, an early substitute for Stuart Armstrong, sent a cross into the box that Griffiths laid off for the Australian, whose neat flick found the bottom corner from eight yards.
Thistle had barely got out of their own half but could have had a penalty seconds before the break following a rare foray forwards.
David Wilson's cross came off the arm of Mikel Lustig, but the stand-in Celtic captain knew little about it and referee John Beaton judged it accidental.
The Jags introduced new signing Mathias Pogba, older brother of Juventus midfield star Paul Pogba, as they looked to make more of an impact in the second half.
But Commons capitalised on poor defending to knock home Celtic's second in the 63rd minute.
A long ball over the top of the Thistle defence came off the shoulder of Callum Booth and Commons nipped in to chip the ball over Cerny and into the empty net.
Cerny did well to prevent Celtic adding to their advantage moments later when he beat away a stinging strike from Griffiths.