A brace from former Dikwena striker Bradley Grobler, as well as goals from Keegan Dolly and Khama Billiat, saw the hosts to a comfortable three points.
Stars netted through a dubious penalty awarded in the first half, converted by Patrick Malokase.
But the visitors always looked second best against an Ajax side who were brilliantly led in midfield by Dutch star Koen van der Laak.
Poor Stars defending saw Dolly pick up a loose ball on the edge of the area and he applied a cool finish to open the scoring on eight minutes, celebrating his first ever top-flight goal.
Dikwena equalized on 28 minutes through Malokase’s penalty, but it was just a brief respite as Ajax took the lead again through Grobler.
Van der Laak played what looked like a harmless ball across the box but after Obert Moyo failed to clear, if fell to the feet of the Bafana striker, whose shot beat the goalkeeper.
The Urban Warriors should have extended their lead minutes later when the brilliant Van der Laak’s storming run down the right ended with a ball across the face of goal that fell to Paul Rusike at the back-post but, with an open net gaping, he somehow put his effort wide.
Fine trickery from Thuso Phala on the left saw him cut inside and unleash a powerful drive that only just cleared Sean Roberts’ goal.
But it would be the home side who scored next – Dolly’s low cross from the left was not cleared, allowing Grobler a simple tap-in from six yards.
And the cherry on top came in the form of a fourth from Billiat as he sped onto a ball from Rusike and beat the goalie with a clever chip.