Goals from Knowledge Musona and Reneilwe Letsholonyane either side of the break saw the Amakhosi pick up the points, leaving them just three behind log leaders Orlando Pirates and Ajax Cape Town.
United now find themselves in a relegation dog-fight, but they only have themselves to blame after yet again failing to make their dominance count.
SuperSport did start a little slowly and fell behind in the 15th minute when Musona found the back of the net. Letsholonyane won the ball in midfield and played a swift pass to Siphiwe Tshabalala, who cleverly slipped the ball through to Musona and left him with only Rowen Fernandez to beat, which he did with ease.
After that SuperSport found their footing and almost hit back immediately through Fikru Tefera, but he was denied by a fantastic save from Itumeleng Khune.
As the half progressed United’s presence became more pronounced and they certainly ended the stronger of the two sides.
The second half was more of the same and saw United with the lion’s share of possession.
But the closest they came to finding an equaliser was in the 70th minute when Thabo September attacked down the right and whipped an inviting cross into the box. Magogi Gabonamong did well to rise between two defenders to meet the ball with his head, but his effort went inches wide.
Two minutes before full-time the result was put beyond doubt when Letsholonyane found Chiefs’ second goal.
A quick counter-attack saw Abia Nale break down the left before providing a pass to Yeye, who made no mistake from the edge of the area, though Fernandez should have done better.