The SuperSport goals were scored by Ashley Hartog and Kermit Erasmus while Lehlohonolo Majoro scored for Chiefs.
United are now just one point behind log leaders Orlando Pirates and have the fate of their title hopes in their own hands, as they face both Pirates and Mamelodi Sundowns in two of their remaining three games.
The visitors started the game very strongly, forcing Chiefs onto the back foot, though they were unable to create any clear chances. Amakhosi soon got their passing game going, but apart from one sharp save by Ronwen Williams from a quickly-taken free kick, they offered little in attack.
On 39 minutes SuperSport deservedly broke the deadlock. A Kermit Erasmus free-kick found Thabo September at the far post and the defender produced a fine header back across goal that hit the crossbar, before Ashley Hartog forced the ball home on the rebound to make it 1-0.
It took just 10 minutes of the second half for United to double their advantage. Erasmus let fly with a shot from long range that swerved viciously and left Khune rooted to his line, helpless to try and make a save.
At 2-0 up it seemed that SuperSport would cruise to an easy victory, but any thoughts of that were erased on the hour mark when Chiefs pulled one back. Substitute George Lebese provided a good cross from the left, Lucky Baloyi saw his goal-bound effort blocked by a defender, but Lehlohonolo Majoro was on hand to fire home the loose ball from close range.
Substitute Sthembiso Ngcobo almost levelled the game on 77 minutes, arriving late in the middle of the box to meet a Majoro cross from the right flank, but the striker was unlucky to see his effort cannon back off the underside of the crossbar.
Ngcobo came close again in the dying minutes, with a deflected effort that forced Williams into tipping the ball over the crossbar, and that was as close as Chiefs came to an equaliser.