Abia Nale opened the scoring, but goals from Takesure Chinyama and Mpho Makola meant that Ajax needed an equaliser by Toriq Losper earn a share of the points.
The Urban Warriors were looking to draw inspiration from their 4-2 win over Free State Stars on Sunday, and Jan Versleijen certainly went on the offensive, starting with an attacking trio of Abia Nale, Khama Billiat and Lebogang Manyama.
All three had found the back of the net against the Ea Lla Koto and were looking to do the same against Pirates.
Lucky Lekgwathi made his 300th start for the visitors, but it was an inauspicious start to his milestone match, as both teams barely had time to settle before Senzo Meyiwa was picking the ball out of the back of the net.
Andile Jali, who was in doubt for the fixture, gave away possession in the middle of the park, and the ball fell to Billiat, who supplied a through ball to Nale. The Kaizer Chiefs loanee slotted it past Mewiya in the seventh minute.
Pirates then had the perfect opportunity to draw level through Thabo Matlaba, who had just the keeper to beat, but he skied his effort over the crossbar.
Lekgwathi nearly turned the ball into the back of his own net, in the 20th minute, when he intercepted Billiat’s cross into the box, but fortunately for him it went wide.
Ajax’s magic continued in the 40th minute, when their attacking trio played some great passing football. Manyama sent in a cross, from Billiat’s pass, towards Nale, who made a great run into the box before unleashing a shot which stung Meyiwa’s palms.
Ajax should have extended their lead a minute after the interval when Billiat went one on one with the keeper, but he panicked and rounded the crossbar.
Pirates then drew level in the 49th minute, when Chinyama left Sander Westerveld flatfooted in goal and nodded home a cross.
Bucs claimed the lead four minutes later, when substitute Makola cracked home a rebounded ball.
It was do or die for Ajax and they opted for the former when they responded with a goal, on the hour mark, when Losper received a ball from Manyama and beat his marker to tap home from six yards out.
An opportunity to close the game fell to Billiat once again, when he and Manyama combined beautifully around the box, but like most of his efforts on the night it was wide.