Tefu Mashamaite had given Chiefs a fourth minute lead from a corner-kick.
Joshua Obaje levelled matters just before the break from a quick counter before Nkhatha netted to restore Chiefs' lead on 65 minutes, and Lucky Baloyi's goal in injury time made sure of the three points.
It was a valiant display from Leopards, but that could not earn them the points.
Amakhosi were given a boost in the match as Morgan Gould returned to starting line-up after his six-month injury lay-off.
In the fourth minute Siphiwe Tshabalala did well to deliver a corner kick to Gould inside the box and it was the defender who directed the effort to Mashamaite, with the centre-back making no errors in putting it past the goalkeeper.
In the 18th minute Leopards showed some urgency in their search for the equaliser and Mongezi Bobe tested Itumeleng Khune from the left of the byline.
Then the Chiefs shot-stopper pulled off the save of the match in the 23rd minute, when he pushed Brian Amidu’s effort onto the upright before gathering the rebound.
Leopards were putting Chiefs under pressure and they tested their luck through Djunga Munganga, who had a shot from 30 yards on the half hour mark.
And their insistence paid off when Obaje beat Khune at the near post with an easy tap-in three minutes from the half-time break.
Abel Makhubela opted to make a change at the start of the second half, bringing on David Zulu in place of Amidu.
Azwindini Maphaha was forced into making a save off Bernard Parker’s 60th minute set-piece, and five minutes later Chiefs put themselves ahead for the second time.
Reneilwe Letsholonyane supplied a through-ball to Nkhatha, who struck it first time with a powerful shot, which shook the back of the net despite Leopards’ goalkeeper having got his fingertips to it.
Despite the pressure from the home side, Chiefs left Polokwane with the glory, when a goal from the substitute Lucky Baloyi in the 94th minute sealed the win and left Stuart Baxter’s side smiling.