First-half goals from Milton Ncube and Erwin Isaacs handed the Urban Warriors their first win of 2015 as they climbed up to fifth in the Premiership standings.
The visitors created the first chance of the game on nine minutes when neat link-up play down the left flank led to a chance for Ruben Cloete, but he fired wide of the mark from inside the area.
However, just three minutes later Roger De Sa's side broke the deadlock with their first chance as Chippa goalkeeper Mbongeni Mzimela could only parry Franklin Cale's free-kick into the path of Ncube, who was left with an easy tap-in from close range.
And the hosts went on to double their lead on 19 minutes when Erwin Isaacs played a one-two with Cale before the striker drilled his shot beyond Mzimela from 25 yards out.
Kristopher Bergman should have halved the deficit shortly before half-time after he found space inside the area, but his header lacked power and Ajax keeper Anssi Jaakkola was able to gather the ball easily.
The Urban Warriors took a two-goal into the break and were less adventurous in the second half as they appeared happy to soak up the pressure from Chippa.
Ernst Middendorp's men fashioned two early chances inside the opening 10 minutes, but Jaakkola made easy work of William Twala's efforts on both occasions.
Jaakkola was called into action again on 76 minutes as he kept out a strike from George Akpabio from inside the area to maintain his team's two-goal cushion.
The Mother City outfit finally got a sniff at goal in the final minute of the match, but Robin Ngalande failed to hit the target with his lob, with only Mzimela to beat, although in the end it was a welcome win for Ajax.