The Pirates goals were scored by Bennett Chenene and Lucky Lekwathi, while Thembinkosi Fanteni scored for Ajax in the first half.
The rain poured down for virtually the whole game which made for tricky and slippery conditions. Both teams played well but Pirates did look the better side during the second half after they got the equaliser.
In the 12th minute Pirates should have taken the lead when Chenene ran down the left and crossed the ball to Excellent Walaza in front of goal only for the striker to hit his shot wide of the post from about 10-yards out.
The visitors nearly scored in the 24th minute when an Aidan Jenniker shot from inside the box thundered against the bar from a low cross by Russel Mwafulirwa.
Ajax took the lead in the 28th minute when Senzo Meyiwa blocked a shot from Mwafulirwa, the ball rebounded out to Fanteni who scored with a shot from inside the 18-yard area.
Meyiwa saved well from a free-kick by Eyong Enoh in the 51st minute when he punched the ball over the bar.
Jenniker took a shot from the left and it was well blocked by Meyiwa in the 58th minute.
In the 66th minute Pirates equalized when Chenene scored with a header from a cross by Lebohang Mokoena on the right.
Pirates took the lead in the 79th minute when Lekgwathi scored with a header from a Chenene corner giving Hans Vonk no chance.
In the 94th minute Ajax nearly got the equalizer when a header from Eduardo Ferreira hit the post from a corner-kick taken by Nhlanhla Shabalala.