Tashreeq Morris scored the winning goal deep into stoppage time to send the Athlone Stadium crowd into raptures.
Thuso Phala gave the away side the lead in the 38th minute, slotting past Anssi Jaakkola one-on-one after brilliant build-up play and a quality throughball from David Mathebula in midfield.
Phala had a glorious opportunity to make it 2-0 a minute before half-time when the ball fell at his feet eight yards out but he got his technique all wrong and sliced his first-time shot in the side-netting when he should have scored.
Substitute Lebogang Manyama had another good chance after a skillful first-time through-flick from Jeremy Brockie played him clean through on goal, but the former Urban Warriors man stumbled over his own feet when he would have been one-on-one with Jaakkola.
Those chances would come back to haunt SuperSport as Mosa Lebusa equalised five minutes from the end with a drilled shot into the bottom-right corner after great persistence from Franklin Cale to set up the chance, poking the ball through for him from just outside the box.
Then came the drama as Nazeer Allie's pinpoint cross from the right flank found substitute Morris steaming in and he buried his header past Williams from close range to send Ajax into the Nedbank Cup Final.