Substitute Zulu got onto the end of an excellent cross from the right wing and slammed the ball home in the 84th minute, in one of the few occasions when either team's defence was turned around to face their own goal.
Towering defender Khoza, meanwhile, mopped up everything that Amakhosi could muster in attack and was deservedly the Man of the Match.
Leopards' first chance came in the 20th minute when a free-kick was spilled by Arthur Bartman, only for Kingston Nkhatha to miss with the rebound.
But their best chance of the first stanza came in the 28th minute when Rodney Ramagalela crossed to Kingston Nkhatha who got in between two defenders, but mistimed his header.
Leopards were in control in the first half and it took 35 minutes for Chiefs to get a proper shot at goal when Lucky Baloyi took a long range effort, but it flew high without any real power.
Then, in the 42nd, Willard Katsande struck a long range shot with his left, but merely forced Posnett Omony into a save.
In the 63rd minute, Chiefs had a great chance when Parker missed the target following a Tshabalala pass, but credit must again go to Khoza who did enough to put Parker off.
Vermezovic made his third and final change in the 64th minute, taking off defensive midfielder Baloyi and bringing on striker Sthembiso Ngcobo. But still Chiefs huffed and puffed in the final third of the field.
Lehlohonolo Majoro got two chances in the space of a minute during the last 10 minutes of the game, but he could not find the target on both occasions and Leopards went home with maximum points, and deserved everything they got.