It was a match in which home side dominated, but they battled to turn possession into goals. Despite Lehlohonolo Majoro's early opener, Amakhosi almost allowed a disjointed Arrows back into the game.
Had it not been for Nkhatha extending the lead and giving Chiefs some breathing space, there could well have been some nervy moments for Stuart Baxter.
The opening chance of the game arrived in the second minute when Majoro flicked a shot goalwards from Siboniso Gaxa's supply, only to see Pavels Steinbors tip it out for a corner. Chiefs meant business and they were to go on the attack from then on.
Zambian Justine Zulu shot straight at Khune on 11 minutes, but after that Chiefs went on the rampage and really should have been 3-0 ahead at half-time.
Majoro opened the scoring with a brilliantly curled shot past Steinbors' grasp, after being supplied by Tshabalala.
Three minutes later Majoro got on the end of an inviting cross from the right, but could not get enough of his head on the ball.
In the 25th minute Philani Shange thought he had won a penalty for Arrows when he went down inside the danger area, after making a good turn. But the referee felt he went down too easily and he was booked instead.
Chiefs went close on half an hour, when Siyabonga Nkosi got up high to flick a header at goal, but Steinbors moved quickly to tip the ball around his upright.
Abafana Bes'thende came back into the game in the second half and substitute Thamsanqa Gabuza got free and blasted a shot way over the bar.
But Nkhatha made the game certain for Chiefs when he got onto the end of a long ball over the top that caught the Arrows backline flat.
The Zimbabwean pounced again in the 83rd minute when he showed a good touch on the run before powering in a shot, which beat Steinbors at his near post.