In front of a packed house, the Amakhosi created the better chances and will feel disappointed at not having claimed all three points on offer, though Phunya Sele Sele were resilient opponents who claimed their first away point of the season thanks to a great showing from goalkeeper Patrick Tignyemb.
Chiefs dominated the early stages and should have taken the lead on 10 minutes when George Lebese was faced with only the goalkeeper to beat, but he hesitated and was quickly closed down by Patrick Tignyemb and his defenders.
The hosts really put Celtic’s defence under siege in the first quarter hour or so, but the men in green and white kept their composure well and weathered the storm, before establishing a foothold in the game.
In fact, Phunya Sele Sele had arguably the best chance of the first half. A ball fell kindly for Lerato Manzini in the penalty area but he shot straight at Itumeleng Khune when presented with a clear sight of goal.
The first half ended with the score line blank and neither goalkeeper having made any saves of real significance or difficulty.
The second half followed a similar pattern to the first until about 20 minutes to play when the Amakhosi suddenly upped the tempo and began to put Celtic under enormous pressure at the back.
Bernard Parker almost netted his eighth goal of the season with a delicate touch off a low cross from Lebese, but the ball rebounded off the inside of the upright before being hacked clear of the danger zone.
On the 70 minute mark Lehlohonolo Majoro controlled a superb long pass from Lebese, but his effort on goal was bravely blocked by Tignyemb, who had moved quickly off his line to close down the angle.
With nine minutes to play Celtic created another clear scoring chance when substitute Mduduzi Nyanda brought down a cross before making an angle to shoot on goal, but again the effort was straight at Khune.
On 89 minutes Reneilwe Letsholonyane executed a neat turn and shot in the Celtic penalty area, but his goal-bound effort was brilliantly saved by Tignyemb, while in injury time Majoro shot just wide from the edge of the box.