The hosts took a two-goal cushion into the break thanks to Cecil Lolo and Tashreeq Morris, and while Stars gave an improved second-half showing, all they had to show for their efforts was an own-goal from Rivaldo Coetzee 10 minutes from time.
After a strong start to the game that saw the home side making most of the play, the Urban Warriors took a deserved lead on 15 minutes when Lolo fired in a swerving left-footed shot which left Stars keeper Kabelo Dambe grasping at thin air.
Stars were battling to make any openings in the Ajax defence, with home keeper Anssi Jaakkola not having to make any serious saves.
At the other end of the field, the Cape side were always looking good for another goal and it arrived after 27 minutes when Franklin Cale picked out Morris with a free-kick; the striker slotting home from close range with a first-time shot.
The remainder of the first half passed without much incident as Ajax shored up their defence and midfield to make sure that their lead stayed intact.
After the restart, the two sides found themselves more evenly balanced, with both teams struggling to find any kind of fluency or rhythm in their games.
Dikwena’s Letladi Madubanya brought out a fine reflex save from Jaakkola in the 68th minute, with the visiting side finally getting on the score-sheet in the 79th minute when Coetzee deflected a cross into the back of his own net.
Any thoughts of a late Stars comeback, however, came to nothing as the Cape side held on for the win that takes them into second spot on the standings.