Celtic looked to get off the perfect start and they nearly did that in the third minute when Lantshene Phalene sent a low effort just wide of the upright.
Stars carved out a chance of their own in the 11th minute but Thabo Maphakisa dragged his effort wide of Patrick Tignyemb's upright.
Eight minutes later, Deon Hotto was presented with a chance but he sent his effort high and wide as Celtic continued dominate.
The home side eventually took the lead after 30 minutes with Victor Letsaolo finding the back of the net, 0-1.
Luc Eymael's charges failed to threaten in the final stages of the opening stanza and went into the break trailing.
Nhlanhla Vilakazi was introduced for Relebogile Mokhuoane at the start of the second half, with the visitors looking get back on level terms.
Celtic picked up from where they left off in the first half, as Lucky Baloyi bagged his second goal of the season to double his side's lead in the 57th minute.
The home side continued to dominate and they eventually extended their lead when Letsaolo fired past Sangare to complete his brace in the 64th minute.
Veselin Jelušic introduced the likes of Given Mashikinya and Kabelo Mahlasela for the final 20 minutes as Celtic looked to run down the clock.
The final stages of the second half proved to be a quiet affair as Celtic held on to claim a the win, which sees them move up to fourth spot.