The result leaves the Urban Warriors just two points clear of Supersport United, who have a game in hand. Matsatsantsa host Free State Stars at Super Stadium on Sunday.
Enoh Eyong scored for Ajax Cape Town, while Tshepo Ramokala netted for Stars.
The hosts dominated proceedings early on with Russell Mwafulirwa forcing visiting keeper Wayne Sandilands into a good save to deny the striker’s volley from hitting the back of the net in the fifth minute.
However, Platinum Stars almost caught the Urban Warriors on the break in the 13th minute, but Phumudzo Manenzhe sent his header, from Koketso Mmotong’s cross, straight at home keeper Hans Vonk.
The hosts took the lead in the 26th minute when Eyong capitalised on a defensive error by the visitors to blast the ball into the far corner from outside the area.
Although Stars didn’t look like seriously threatening the Ajax goal for the rest of the half, they managed to level matters a minute before the break through Ramokala, following a good cross by Ivan Zwane.
The score remained 1-1 at the break.
The Urban Warriors continued their dominance in the second half and went close five minutes after the restart with Mwafulirwa heading substitute Granwald Scott’s cross just over the bar.
Mwafulirwa should have put the hosts ahead in the 63rd minute when he received a pass from Scott inside the area, but the striker sent his close range effort high over the bar.
The game then became a stop-start affair due to a number of fouls committed by both teams, combined with a number of substitutions, culminating in a break in momentum for both sides.
Ajax won a number of corners in the dying minutes, but they could not find a way past the solid Stars defence, with Ajax substitute Makhanyiseli Siwahla receiving a red card in the final minute of the game for retaliation following a challenge by Ramokala, who received a yellow card from referee Ace Ncobo.