Pirates coach Milutin 'Micho' Sredojevic made three changes to the starting that faced Baroka FC in their previous league match which ended in a 1-1 draw two weeks ago.
Happy Jele and Bernard Morrison returned to the Pirates starting line-up, while Mothokozisi Dube made his official debut for the Buccaneers.
Stanley Menzo, the Ajax coach, fielded a strong team as the Urban Warriors targeted their first league win of the season after losing 2-0 to Maritzburg United a fortnight ago.
Pirates went into this encounter hoping to continue ther dominance over Ajax as they had collected four points from Urban Warriors in the league last season.
The hosts got off to the best possible start as they took the lead through Morrison just nine minutes into the match after Ajax were caught napping in the box.
A long throw in found the Ghanaian forward unmarked in the area and he fired past goalkeeper Brandon Petersen to make it 1-0 to Pirates.
This was the former AS Vita Club attacker's first goal for Bucs as he battled for regular game time last season and he has since been given a chance to prove himself by 'Micho'.
The Urban Warriors' midfield which included Tercious Malepe, who is on loan from Pirates, was struggling to contain Morrison, who was making dangerous runs into the visitors' box with the hosts dominating possession.
However, newly appointed Ajax captain Mosa Lebusa and his team-mates managed to contain the Buccaneers and the score was 1-0 to Pirates at half-time.
Ajax had to find a way to unlock the Bucs backline in the second half - having failed to score in their last visit at Orlando Stadium as the match ended in a 0-0 draw last season.
The Urban Warriors came back a rejuvenated side following their team talk with Dutch tactician Menzo and visitors pressed the Buccaneers in the early stages of the second-half.
His counterpart Sredojevic responded by introducing Thembinkosi Lorch, who was expected to terrorize the Ajax defence with his pace and tricks in the final third.
Lorch was tightly marked by Erwin Isaacs, who has flourished as a right-back having started his career as a winger-cum-striker at former PSL champions Santos.
Pirates managed to regain control of the match and the home side thought they had doubled their lead when Thamsanqa Gabuza scored from close range after the hour-mark, but he was ruled offside.
With Ajax attacking in numbers in the closing stages, Sredojevic made a tactical change - pulling out Mpho Makola for Abbubaker Mobara and Bucs played with five at the back in the late stages of the match.
Pirates were able to contain Ajax in stoppage time with keeper Wayne Sandilands denying Lebusa with a great save and the match ended in a 1-0 victory in favour of the hosts.