The result denied the Urban Warriors a place in the top eight of the log, while the Chilli Boys remain in sixth place.
The teams traded chances in the opening quarter of the match, though goalkeepers Anssi Jaakkola and Daniel Akpeyi were largely untroubled.
Ajax claimed the lead just before the half-hour mark through Nxumalo, with the striker netting his 11th goal of the season in the 29th minute as he received a slightly deflected pass from Tashreeq Morris with a hint of unspotted handball, composed himself and slotted past Daniel Akpeyi on his left foot.
The closest Chippa came to a reply in the first half saw attacker Manzini strike an effort over the target direct from a free kick just before the interval.
After a quiet opening period of the second stanza, in which there was little in the way of goalmouth action, Chippa levelled the game on the hour-mark thanks to Manzini, who pounced on a poor giveaway at the back, cutting inside the last defender and finishing with his left foot into the top-right corner past a stranded Anssi Jaakkola.
A few minutes after conceding the equaliser, the Urban Warriors very nearly reclaimed the lead through Nxumalo, who shot just wide of the target – much to Akpeyi’s relief.
Ajax kept up the pressure on Chippa’s goal as the second half wore on, with Nxumalo and Morris both going close to a goal, but ultimately the Cape side were left frustrated and had to settle for a share of the spoils.