Both Thulani Hlatshwayo and Sibusiso Zuma saw penalties saved late on, but earlier goals from Eleazar Rodgers and Aiden Jenniker meant Sibusiso Zuma’s 86th-minute strike proved nothing more than a consolation.
The Urban Warriors got off to a positive start and had the ball in the back of the net in the second minute after Rodgers nodded home a cross, but play was brought back for a foul on Bevan Fransman.
Rodgers and Lebogang Manyama both sent shots wide, before Bennet Chenene followed suit at the other end.
Lance Davids was lucky to get away without a booking midway through the first half after he laid on a heavy studs-up challenge onto the ankle of Chenene.
But Ajax’s hard work was rewarded when they deservingly grabbed the lead in the 38th minute through Rodgers, who sliced home Manyama’s cross to score his first goal for the Urban Warriors.
Visiting goalie Anssi Jaakkola, who had little to do for the opening hour of the game, did well to deny Mor Diouf the equaliser by tipping the shot over the crossbar early in the second half.
SuperSport were putting the pressure on Ajax and it resulted in a dramatic closing 10 minutes which saw two penalties given.
Ajax were the first to be the awarded the spot-kick when Fransman was wrongly judged to have brought down Bantu Mzwakali in the box. Hlatshwayo stepped up, but his attempt was brilliantly saved by Rowen Fernandez.
That seemed to spur the away side on and Jenniker made it 2-0 with a bursting run into the box which saw him slot the ball past the SuperSport keeper at the near post.
But a minute later and SuperSport were handed the smallest of lifelines when Zuma stood up to the penalty area to take the second spot-kick in the match. Like his opposite number, Jaakkola too denied the effort, only to be beaten by Zuma on the rebound.
The home side was then reduced to 10 men inside stoppage-time after Fransman was harshly shown a second yellow on the night, compounding a miserable night for SuperSport.