Goals from Bradley Grobler and a revitalised Jabu Mahlangu handed Stars a 2-0 half time lead, but Celtic hit back in the second stanza thanks to an own goal and secured a point late on when substitute Mark Mayambela scored a dramatic equaliser.
Tshepo Ramokala should have opened the scoring for Stars as early as the seventh minute but, after springing Celtic's offside trap and being faced with only goalkeeper Shu-Aib Walters, he failed to hit the target.
However, the winger was at the heart of the action when the Tycoons broke the deadlock in the 22nd minute. Ramokala cut picked up a long ball before cutting inside and forcing Walters into a good save with a clever curling shot, but Grobler was on hand to force the ball home on the rebound.
Petrus Mahlatsi had a decent chance to bring his side level two minutes later when he ran onto a fine cross from Patrick Malokase, but Stars' Tapuwa Kapini had read the play well and came off his line to make a smothering save from the striker's header.
Kapini was even better ten minutes later when, in the midst of a corner kick that was poorly defended by the hosts, he heroically flung himself in front of a point blank range effort from Shaun Bartlett that looked destined to ripple the back of the net.
Celtic's rising influence in the game was confirmed when they carved out a clear opening for Mzondi Mthombeni in the 38th minute, only for the left-footer to drill the ball wide of goal, and Mahlatsi failed to trouble goalkeeper when he was given the space for a free header from a corner kick two minutes later.
Stars immediately made the visitors pay for their wastefulness, as a simple route-one ball and flick-on saw Mahlangu clean through; the winger easily rounded Walters and stroked the ball into an empty net to claim a debut goal and put his side 2-0 up.
Nine minutes into the second half, Almiro Lobo was probably lucky to get away with just a yellow card from referee Daniel Volgraaf after bringing down Mahlatsi from behind as the last man in defence; a stricter official would have been well within their rights to dismiss the Mozambican.
Just before the hour mark Kapini again came to the rescue of his flat-footed defence, thwarting Solomon Mathe as he tried to get on the end of a chipped ball into the penalty area and then doing enough to put Mahlatsi off as the striker tried to score from the loose ball.
But there was nothing the goalkeeper could do when Phunya Sele Sele pulled one back in the 71st minute. John Maduka floated in a teasing free kick that Lobo could only glance into his own net under pressure from Timothy Batabaire.
Da Gama's team should have made it 2-2 in the 77th when a mistake from Daniel Tshabalala allowed Mahlatsi a sight of goal, but his instinctive stab directed the ball just past Kapini's left hand upright.
It seemed as if it simply was not Celtic's night, but a late turning point came in the game when Lobo received his second yellow card and was given his marching orders in the 85th minute.
The visitors had little time with which to make their numerical advantage count, but they capitalised with just three minutes to play in regulation time, as Mayambela buried a beauty of a shot into the top corner to level the scores.
Celtic actually had chances to win the game in the dying minutes, but Man of the Match Kapini continued his superb vigil right to the final whistle and ensured his team at least got a share of the spoils.
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