The Urban Warriors were looking for their first win under Jan Versleijen, but instead battled to create many chances as they remain stuck in 15th place, with only Chippa United below them.
AmaZulu would have been much happier with the point, which moves them up to 11th.
The match got off to an exciting start with the play flowing freely from end-to-end and it was Ajax who were called into question first when Nazeer Allie had to make a clearance off the line, 16 minutes in.
Moments later the defender performed another great interception when he threw his body in front of Goodman Dlamini’s shot – the 27-year-old lucky to get away with it as replays show it was a hand-ball.
Mabhuti Khenyeza then stung the palms of Tapuwa Kapini with an effort from the edge of the box as the two teams played out the remaining goalless five minutes of the half.
The home side came out commanding the first ten minutes of the second half, winning a series of corners, but failing to make the most of their opportunities in front of goal.
Kugelani Madondo hit a long-range effort wide, while Travis Graham hit his shot over the bar from 15 yards out as chances were few and far between, meaning the two sides had to settle for a share of the spoils.