Teboho Moloi's charges nearly took the lead on 12 minutes when Paseka Mako sent a header just wide of Jody February's upright.
Daniel Akpeyi was called upon four minutes later as the Chippa shot-stopper produced a good save to deny Tashreeq Morris from a tight angle.
Chippa squandered another chance on 20 minutes as Sizwe Mdlinzo fired wide of the upright from close range.
The visitors were made to rue that miss as Ajax took the lead seven minutes later courtesy of a thumping strike from Thabo Mosadi, 1-0.
It got worse for Chippa four minutes before the break when Zitha Macheke was sent for a dangerous challenge on Mosadi.
The Urban Warriors picked up from where they left off in the first half but the likes of Bantu Mzwakali and Morris failed to convert their chances in the opening 10 minutes.
February came to Ajax's rescue in the 58th minute as he burst off his line to deny Moeketsi Sekola in a one-on-one situation.
The chances continued to fall for Ajax and they squandered another one on 68 minutes when Mzwakali failed to hit the target from close range.
With 10 minutes remaining, Menzo introduced Junaid Sait for Roscoe Pietersen as Ajax looked to protect their lead.
Chippa had to finish the game with nine men after Akpeyi was given a straight red card in second-half stoppage time for a tackle on Mosadi.
Nonetheless, the Urban Warriors managed to hold on for the win, which ends their winless run.