Ngcobo poked home midway through the opening half, which was enough for the Clever Boys’ first win at home in the league this season.
Wits remain unbeaten after three games, while the Team of Choice suffered their first defeat of the season, following a win and a draw from their opening two fixtures.
Wits got off to the brighter start, despite a dull opening 20 minutes.
Ngcobo, however, changed all that and sent the hosts into the lead after a goalmouth mix-up allowed the prolific goal poacher to stab home a loose ball, to hand Wits the advantage in the 22nd minute.
Ngcobo was proving to be a handful and was denied a second by a more alert Walters in the 36th minute, the goalkeeper punching away a fierce right-footed effort from inside the area.
Leading at the break, the hots came out in the second period hungry for more of the same.
Ngcobo was at the centre of all of Wits’ attacks and twice headed wide of the mark as United retreated and looked in danger of disappearing out of the contest all together.
Ashley Hartog’s effort was the closest United would come in the second half, but for a post in the way, after a thunderous effort from the veteran midfielder on 75 minutes.
In the end, the hosts bagged a deserved result despite missing a handful of chances.