Thuso Phala gave Matsatsantsa the lead just before half-time, but the Urban Warriors would leave it late to stage a comeback as Mosa Lebusa and Tashreeq Morris struck in the final five minutes to clinch victory.
After a lively opening that produced no chances Ajax goalkeeper Anssi Jaakkola was tested twice in quick succession when he punched away a free-kick from Daine Klate on 14 minutes before making a low save to deny Jeremy Brockie from close range two minutes later.
The hosts threatened on 20 minutes when Nathan Paulse raced through on goal, but United keeper Ronwen Williams rushed out to deny the striker, before Travis Graham blazed his effort over the crossbar.
Phala almost grabbed a second goal moments before half-time, but Ajax were relieved to see his shot hit the side-netting only.
Roger De Sa's men made a bright start after the restart but failed to create anything of note.
The contest then entered a lull as both teams made numerous substitutions, which disrupted the flow of the game.
If SuperSport thought they had done to win enough they were in for a shock as the Mother City outfit hit back twice at the death.
First Lebusa fired home an angled shot from inside the area with five minutes left, before Morris popped up deep into stoppage time to beat Williams with his header from Nazeer Allie's cross.