A great header from Moses Spandeel handed Celtic the points.
The team in green and white had beaten their rivals by the same scoreline in the last three Premiership meetings, from the second half of the 2009/10 season.
The win is Celtic’s first since mid-August, breaking a five-game winless streak. They have moved up to seventh on the table on 11 points. Stars are ninth, with the same points tally but an inferior goal difference.
A scrappy first half ended with Phunya Sele Sele a goal to the good thanks to Spandeel’s header three minutes before the interval.
Ea Lla Koto dominated the second stanza but were unable to find a way past Celtic’s resilient defence.
The teams cancelled each other out for most of the first half and genuine scoring chances were hard to come by. A fierce midfield battle developed and neither team was really able to really stamp their authority on the game.
However, Celtic took advantage of a rare instance of poor defending from Stars just before the half time break.
Spandeel scored an excellent diving header, ghosting away from his marker before converting a teasing cross to the far post from right-back Kgotso Moleko.
Ea Lla Koto were the first to threaten in the second half, with Dove Wome stabbing a shot wide of the target just under 10 minutes after the restart.
The Togo striker soon suffered a clash of heads with Celtic hard-man Letladi Madubanya but was able to play on despite being knocked out cold initially.
Stars substitute Edward Manqele came close to leveling the game just a few seconds after coming on in the 75th minute, shooting just wide of the near post, though Patrick Tignyemb appeared to have the effort covered.
Manqele had the ball in the back of the net three minutes later, rounding Tignyemb before steering the ball home from a tight angle, but he was ruled offside – television replays suggested that the striker was unlucky to have the decision go against him.
Celtic rarely threatened in the second half but they almost doubled their advantage on 83 minutes, with substitute Danny Venter exchanging passes with Phenyo Mongala before powering through the middle of Stars’ defence, only to steer his shot just wide of the target.