Mandla Masango scored the only goal of the game – a beauty on 79 minutes – in a game which livened up in the second half after a slow first 45.
The Amakhosi came into the match with an unchanged side after four wins on the trot, while Celtic made just the change - new signing Musa Nyatama replacing Dumisani Zama.
It was a cautious start, but the game sprung into action on 10 minutes when Hellings Mhango unleashed a fierce drive towards the top corner. The ball looked to be going in, but Itumeleng Khune pulled off a brilliant one-handed save to keep the scores level.
Chiefs had their first chance on 16 minutes when nice interplay allowed Masango to run into the area. He drove to the by-line and put in a cross, but Alfred Ndengane was on hand to block as the ball ended up on the roof of the net.
Mhango had a good chance soon after when Nyatama lobbed a perfect pass to the Malawian, but his touch let him down, allowing Khune to gather.
The best chance of the half came on 39 minutes when a poor backpass played Kingston Nkhatha in on goal. However, the Zimbabwean delayed his shot, eventually tumbled over, and the chance was lost.
Chiefs started the second half strongly, with Reneilwe Letsholonyane volleying over early on after more good work by Masango, before George Lebese crashed a curling free-kick against the crossbar.
Keegan Ritchie showed some great feet against his former side, beating three players before setting up Lerato Lamola on the edge of the area, but his shot was blocked.
Mhango then had a low shot saved before Nkhatha cleverly set up Lebese with a back-heel, but the winger leant back and fired over to squander a great chance.
The goal eventually came on 79 minutes – and it was one well worth waiting for as great one-touch passing resulted in Masango burying Lebese’s cross on the half-volley.
Just a minute later Mathoho hammered a volley against the crossbar from a corner-kick, but that was it as far as the scoring was concerned.
The result moves Chiefs to the top of the table, ahead of Ajax Cape Town who won 2-1 at Polokwane City.