Amakhosi fluffed an early opportunity after Daniel Akpeyi handled poorly, but both Leonardo Castro and Ryan Moon were unable to punish them.
Chippa got in the mood and managed to get shots on goal from Buyani Sali and Thabo Rakhale, though it did little to trouble Itumeleng Khune.
Chiefs were forced into an early change that jeopardised their game-plan as Ramahlwe Mphahlele had to come off injured, with Bhongolwethu Jayiya on in his place on 14 minutes.
That played into the hands of the visitors, who took the initiative to go in front through Rakhale after out-sprinting Eric Mathoho and beating an on-rushing Khune on 25 minutes.
It put the visitors firmly in the driving seat as they looked threatening and caught Amakhosi on the counterattack.
The hosts looked well out of their depth and went into the break trailing, with a mountain to climb in the second stanza.
Chiefs made another injury-forced change at the start of the second half, with Bernard Parker replacing Teenage Hadebe.
Interestingly, Steve Komphela changed his playing stall, going with an all-attacking approach in a 3-5-2 system.
The Chilli Boys continued to look threatening on the break but were caught out time and again with their high-line approach from the hosts.
Komphela made their third and final change with Dumisani Zuma replacing Jayiya, who also came from the bench on 63 minutes.
The best chance of the half for the Glamour Boys fell to Zuma off a cross from Hendrick Ekstein, but he was unable to head home from right in front of goal.
As expected, it came back to haunt them with a cheeky finish from Mxolisi Machupu following a defence-splitting pass from playmaker Linda Mntambo on 78 minutes.
Amakhosi looked for a consolation in the closing stages but Zuma wasn’t able to beat Akpeyi, who pulled off a good save.
Eventually, substitute Edward Manqele came off the bench and rounded off the victory with a tap-in at the far post in added time.