Moses Spandeel had given Celtic the lead from the penalty spot, before Kaizer Motaung Jnr equalized in the second half to earn a share of the spoils.
Chiefs made the early running and Cyril Nzama, who scored in midweek against Golden Arrows, found himself in space in the box on eight minutes, but slipped as he shot and the ball went harmlessly high and wide.
Tinashe Nengomasha tried a spectacular bicycle-kick two minutes later that also failed to work Shu-Aib Walters in the home goal, while Motseothata November had the first shot in anger at the other end but it drifted wide.
Mark Amofah had a great chance to give Celtic the lead on 22 minutes when he beat the off-side trap and raced clear one-on-one with Itumaleng Khune, who did brilliantly to block the Ghanaian’s shot by showing speed off his line.
David Obua fired in a rocket that was beaten away by Walters on the half-hour mark, and Celtic went up the other end and almost took the lead themselves as the speedy Amofah again found space and his shot was narrowly wide of the upright.
Great play from David Mathebula down the right set up Gerald Sibeko unmarked in the area, but he spooned his shot wide when he really should have hit the target. That was true a few minutes later as well when he shot wildly when again well placed.
But it was Celtic who took the lead a minute before halftime when Nzama upended November in the box and Spandeel sent Khune the wrong way to convert from the penalty-spot.
It looked a fair award, though Chiefs might argue that the initial contact made by Nzama was outside the box.
Amakhosi coach Muhsin Ertugral showed his displeasure with his side at the halftime break when he replaced Obua and Mathebula with Motaung Jnr and Thabo Mooki.
But it was Celtic who had two early openings in the second period, but neither Amofah nor Kukame could make the most of them with some wild shooting.
And the duo should have extended the lead on the hour-mark when Amofah crossed for an unmarked Kukame, who had a simple tap-in, but made a lazy attempt to attack the ball and the chance was gone.
The pattern of the game was becoming clear. Chiefs were throwing men forward in search of the equaliser, with Celtic content to use Amofah’s pace to hit them on the break.
And they were made to pay for that when Motaung Jnr equalised on 72 minutes as he latched onto the loose ball at the back post and his shot on the stretch beat Walters.
Chiefs’ shooting from distance left a lot to be desired and they failed to really test Walters from there on in, despite their obvious superiority in the possession stakes.
And Celtic almost made them pay when substitute Carlo Scott found acres of space down the left, but, with plenty of time to pick out one of the three teammates in the box, instead fired his cross straight at a defender.
Motaung Jnr created a shooting chance for himself in injury time, but his effort was easily saved by Walters.