It was a crucial six-pointer for both the sides, with top eight spots and the opportunities to stave off the drop on the line.
Neither side were able to separate themselves in the opening five minutes, with chances few and far between.
The first shot at goal only came in the 27th minute as Mark Mayambela stepped forward for a free-kick, but his aim to curl it past Jody February didn’t materialize with the ball rising over the top.
Three minutes later, Yannick Zakri left James Okwuosa for dead on the edge of the box before being blocked off from having a crack at goal by a challenge from Paseka Mako.
The latter looked to turn from preventer to profiteer after seeing his shot cannon off the woodwork five minutes to the break.
Rodrick Kabwe and Fagrie Lakay combined near the box and played in Zakri who blasted over the top four minutes later.
After the break, the first change came from Ajax who brought on Grant Margeman for Toriq Losper in the 52nd minute.
Chippa went in front off the boot of Mxolisi Machupu, who made no mistake to turn the ball home off a corner a minute later.
The Urban Warriors were eager not to leave Port Elizabeth empty-handed when Tashreeq Morris got teed up by Morne Nel, but the striker blasted over the bar.
Substitute Samuel Julies went close to grabbing the elusive equalizer, but his attempt was expertly dealt with Daniel Akpeyi who pulled off a fantastic save on 88 minutes.
However, the Mother City outfit eventually pulled the rabbit out of the hat in added time as Zakri pounced on a defensive blunder to finish off easily.
The result sees them sit one point from safety with three matches remaining in the top-flight campaign.