Muhsin Ertugral's charges showed a lot of energy and good movement on the ball going forward but lacked the final pass to trouble the Stars' backline.
Vuyo Mere almost got the opener for Roger De Sa's troops in the 27th minute with a stinging shot from outside the box that was brilliantly saved by Brandon Petersen.
Tendai Ndoro almost got on the score-sheet for Ajax in the 36th minute, but his strike sailed narrowly wide of the upright.
Zama Rambuwane eventually broke the deadlock three minutes before halftime with a header inside the box after a cross from Mere.
The hosts played with more determination for the equaliser in the opening 10 minutes of the second half but Dikwena was resolute at the back.
However, Tercious Malepe eventually brought the home side level in the 73rd minute with a close range finish, 1-1.
Tashreeq Morris made it 2-1 to the Urban Warriors eight minutes before time with a stunning shot inside the box that found the roof of the net.
Ndoro sealed the match for the Ajax in the last minute of regulation time with a powerful strike that gave Dino Visser no chance, 3-1.