Thabiso Nkoana scored the opener after just two minutes while Tashreeq Morris added a second just before the break. Abbubaker Mobara netted a late own-goal to give the hosts some hope, but it was not to be.
The Urban Warriors took the lead after just two minutes when Nkoana found the back of the net after some good work by Travis Graham.
The home side won a free-kick soon after for a foul by Mobara on Puleng Tlolane, but Jabu Maluleke’s effort was saved.
Anssi Jaakkola then pulled off a stunning save to deny Maluleke – and it proved invaluable when Ajax stretched their lead just before the break when Morris got on the end of a cross by Nathan Paulse to tap in from close range.
Just a few minutes into the second half and the visitors were asking questions of Polokwane once more as Paulse got up to win a header, but he sent the ball straight at Dino Visser in goal.
Granwald Scott had a shot sail over and Paulse missed with a free-kick before Mobara scored past his own keeper to ensure a nervy last three minutes.
Tlou Molekwane was then sent off in the dying moments for a second bookable offence before Jaakkola pulled of a late, great save to deny Tlolane and ensure the points for the visitors.
Ajax are two points behind log leaders Kaizer Chiefs, who beat Bloemfontein Celtic on Tuesday night to make it three wins out of three. Ajax have won two matches and drawn one.