Thapelo Tshilo and Siphesihle Nzimande handed Polokwane the win, and they lifted themselves off the bottom of the table for the first time.
In the fifth minute Lebogang Manyama threatened with a free-kick, which he curled just wide of the post.
And he came close again moments later with another set-piece, after Eleazar Rodgers was brought down near the box. The striker’s free-kick this time hit the target but Polokwane goalkeeper Modiri Marumo got a fist to it.
Brandon Petersen, who was man of the match for Ajax against Bidvest Wits, continued with his impressive form when he bravely grabbed Galabgwe Moyana’s cross into the box.
Just before the half hour mark, Moyana’s corner kick met Essau Kenyenda, but this time his effort did not trouble Petersen and sailed over the bar.
The heat looked like it was starting to get to Ajax and Polokwane managed to catch them on the break in the 40th minute, and Tshilo slid in to tap home the opening goal.
He was, however, replaced immediately afterwards, with what was suspected to be an injury-induced rather than tactical substitution.
After having already replaced Michael Kwong for Nathan Paulse midway through the first half, Muhsin Ertugral opted for a further change, bringing on Lance Davids for Rodgers at the start of the second half.
The Urban Warriors were hit with a serious blow with 30 minutes to go, when Petersen was stretchered off with what looked like a serious injury. Anssi Jaakkola was brought on to make his debut for Ajax in goal.
And he conceded his first goal a few minutes later, when Nzimande found the back of the net in the 70th minute.
There was little Ajax could do to make a comeback and the loss means they drop to the bottom of the table.