Terror Fanteni opened the scoring with a penalty on 20 minutes, after Itumeleng Khune was adjudged to have tripped him.
Reneilwe Letsholonyane equalised in the 48th minute, before Lebongang Manyama got the winner for the Urban Warriors on 75 minutes.
AmaKhosi were bright and breezy early on, putting the Ajax defence under immense pressure.
The hosts were lucky to escape in the 11th minute when Bernard Parker’s stinging drive was pushed by keeper Sean Roberts onto the bar.
However, following some sloppy play at the back, the Urban Warriors earned a 20th minute penalty when Fanteni drew Khune into a foul; Fanteni converting the spot-kick with ease.
Chiefs looked to hit back and were unfortunate to see Lucky Baloyi’s teasing cross failing to pick out a teammate, before Thomas Sweswe sent a volley just wide.
Despite having had the better of the opening half, Chiefs went into the break 1-0 down.
Whatever was said in the dressing-room at half-time worked, as Amakhosi levelled matters just three minutes after the restart, Letsholonyane expertly curling the ball past a helpless Roberts.
The game remained tight, with no more than half chances at either end, until the Urban Warriors regained the lead after 75 minutes when the ball broke nicely for Lebogang Manyama, who showed great cool under pressure to poke home a low shot.
Chiefs rallied hard in the closing stages for an equaliser, but Baloyi lacked the power in his shot to beat Roberts, while Tinashe Nengomasha sent a header just over.
There was more late drama to come however as Lehlohonolo Majoro’s header was touched onto the bar by Roberts, as somehow Ajax hung on.