The victory made it 26 domestic matches without defeat for Brendan Rodgers side, with Dedryck Boyata's second-half header moving Celtic 22 points clear of rivals Rangers.
Celtic face Hearts on Sunday and will aim to break the longstanding club record for domestic games unbeaten, set by the Lisbon Lions in the 1966-67 season.
It was the same campaign in which the club won the European Cup, beating Inter 2-1.
The Hoops' win also saw captain Scott Brown make his 400th appearance for the club and Rodgers hailed the achievement of his players.
Congratulations to Brendan Rodgers & his players who have equalled the Lisbon Lions' 26-game unbeaten record from 1966/67— Celtic Football Club (@celticfc) January 25, 2017
"If you had mentioned it when I first came in to supporters or the players, they might not have believed it," Rodgers told reporters. "A huge honour.
"Huge testament to the players and how they work on a day-to-day basis, along with their professionalism. I didn't mention it so much before the game as you have to do your job, work well and get the result.
And congratulations to captain Scott Brown, who will be delighted to mark his 400th Celtic appearance with a victory. #Brown400— Celtic Football Club (@celticfc) January 25, 2017
"50 years since it was set and think of all the great managers and players who have been at the club, it shows you difficult it is."