The victory is a first in 2017 for Ajax and moves them four points clear of Baroka FC in the relegation play-off position.
After a slow start, it was Ajax who grabbed the initiative as veteran winger Mayambela produced a moment of magic on nine minutes to lift the ball over Tapuwa Kapini in the Highlands Park goal and give his side the lead.
The visitors had a chance to hit back almost immediately when Peter Shalulile flashed his header wide when it seemed easier to score.
But Mayambela was a constant thorn in their side and he almost teed-up a second for Thabo Mosadi, but the latter just failed to latch onto his cross.
Highlands should have drawn level two minutes before the break when Brandon Theron had the goal gaping in front of him, but steered his shot wide of the target.
Collins Mbesuma made a return from almost five months on the sidelines for Highlands with 12 minutes to play, but put a good headed chance over the crossbar.