Tshegofatso Mabaso had a great opportunity to open the scoring for Siwelele in the sixth minute after a square pass into the six-yard area but he blasted his strike over the bar at the near post.
Mabaso had another chance for Phunya Sele Sele in the 14th minute after going through on the right side of the box but his diagonal shot into the bottom corner was parried away by Amakhosi goalkeeper Bruce Bvuma.
Dumisani Zuma had a cracking strike for Giovanni Solinas’s charges in the 26th minute from outside the box that would have been a collector’s item had it gone inside but his curling effort crashed against the bar.
Khama Billiat eventually broke the deadlock for Chiefs 10 minutes before the break, slotting a low shot past Celtic shot-stopper Patrick Tignyemb after going clear inside the box, 1-0.
Siwelele were threatening to find the equaliser in the closing minutes of the first stanza but they could not get clear chances as Amakhosi took the 1-0 lead into the break.
Chiefs were having the lion’s share of possession 10 minutes into the second stanza but Siwelele were compact at the back.
Solinas’s troops were solidifying their rhythm after the hour-mark, looking for that killer pass but the visitors were not offering them spaces for through balls.
The through ball did come in the 64th minute as Leonardo Castro sent Khotso Malope clear to double the lead for Amakhosi with a looping strike into a gaping net after rounding Celtic goalkeeper Tignyemb, 2-0.
Menzi Masuku pulled a goal back for Celtic 15 minutes before time with a strike from the penalty area after the hosts failed to clear a looped cross.
Ndumiso Mabena completed the comeback for Steve Komphela’s men 12 minutes before time with a sweeping half-volley from inside the edge of the box making it 2-2.
Chiefs were back to square one and looking to squeeze the winner five minutes before time but Komphela’s men were compact at the back.
Siphelele Ntshangase had a good chance to net the winning goal for Amakhosi in stoppage time after going through inside the box, but he fluffed his opportunity dilly-dallying and the two sides shared the spoils.