Chiefs were the better side in the first half, but failed to hit the target despite creating numerous chances.
Early on, Morgan Gould couldn't keep his header down from Siphiwe Tshabalala's corner.
In the 12th minute, Shabba delivered the ball in the box from another corner and Celtic's defence failed to clear. The ball fell to Willard Katsande, whose right-footed attempt was over the bar.
Two minutes later, Itumeleng Khune played a long ball and Kingston Nkhatha had a great first touch, but then rushed and his shot was not even close to the target.
Celtic, who were in the backfoot, finally had their chance to test Khune in the 26th minute when Joel Mogorosi tried his luck from outside the box after Gould failed to clear. Khune, however, didn't even have to make a save as the shot went wide.
The home side was forced to make a change with nine minutes before the interval when Trevor Lamola signalled to the bench that he was unable to continue because of an arm injury. He was replaced by Ruzaigh Gamildien.
In the 41st minute, George Lebese played in a great cross but Reneilwe Letsholonyane header over the bar.
There was still more time for Celtic to go on the attack of their own. Vuyani Ntanga let rip from distance and Khune spilled the ball, but lucky for him Chiefs' defence cleared the danger.
After the break Chiefs continued to surge forward in search of the opener.
Tshabalala played a pass to Knowledge Musona who was rushing into the box. The Zimbabwean beat Clayton Daniels, but fluffed the opportunity with an ambitious shot that went accross goal in the 48th minute.
Celtic were forced into another change in the 50th minute, with the injured Walter Letlabika making way for Limbikani Mzava.
It could have got worse for Phunya Sele Sele in the 55th minute when Mogorosi, who was already sitting on a yellow card, escaped a red for a foul on 'Yeye'.
On the hour-mark Siboniso Gaxa was forced off and replaced by Josta Dladla.
Gamildien almost put Celtic in the driving seat, but his well-taken shot just missed the target.
In the 68th minute, Daniels handled the ball on the edge of the box, but Shabba's free-kick was way over the bar.
Letsholonyane could have snatched all three points for Amakhosi at the death but, from a cross by Musona, the midfielder arrived late in the box and failed to control his header.