Milutin 'Micho' Sredojevic decided to name an unchanged starting-line with the Buccaneers having edged out Lamontville Golden Arrows 2-1 in their previous game which was played at the Princess Magogo Stadium two weeks ago.
The Serbian tactician deployed a 4-3-3 formation with Musa Nyatama, who was facing his former side, starting alongside Marshall Munetsi and Xola Mlambo in central midfield, while in-form Thembinkosi Lorch was part of the front three.
Micho's counterpart and countryman, Veselin Jelusic included former Bucs players Jacky Motshegwa and Ndumiso Mabena in the Siwelele starting line-up as they looked to record their second consecutive win in the league.
The Buccaneers dominated the match from the start with new South Africa international Lorch causing havoc for the Phunya Sele Sele defence with his blistering pace and superb skill as the Soweto giants searched for an early goal.
The hosts have scored 19.4% of their goals between 15-30 minutes this season. So, it did not come as a surprise when broke the deadlock 16 minutes into the game.
Justin Shonga played a well-taken corner-kick into the Celtic box and Nyatama rose highest to head home to make it 1-0 to Pirates as the central midfielder haunted his former employers.
Pirates looked dangerous every time they launched an attack and Lorch forced Celtic goalkeeper Patrick Tignyemb into a fantastic save with a powerful long-range shot.
Phunya Sele Sele were struggling to unlock the Bucs defence which was marshalled by Happy Jele, who was making his 200th appearance in the league on the night.
The lanky defender did well to stop his former team-mate Mabena, before the latter could test Pirates keeper Siyabonga Mpontshane following a rare attack by the visitors in the closing stages of the first half.
The score was 1-0 to Pirates at the interval following a first half which was dominated by the hosts.
Celtic, who have netted 20% of their goals between 45-60 minutes, stunned Bucs four minutes into the second half as they levelled matters through Kaizer Chiefs loanee Lorenzo Gordinho , who scored from a corner-kick.
Micho reacted by pulling out Munetsi and he opted for a centre forward in Thamsanqa Gabuza as the Buccaneers looked to benefit from the former Arrows marksman's aerial strength.
Memela played a dangerous curling corner-kick inside the Celtic box and Gabuza pounced, but former Cameroon under-23 international Tignyemb was quicker, and he punched the ball away.
Nicknamed Ganda-Ganda, Gabuza continued to make his presence felt and he was brought down by Gordinho while clear on goal. Celtic were immediately reduced to 10 men as Gordinho was sent off for a late challenge.
The hosts then took advantage of their numerical superiority as Augustine Mulenga made it 2-1 to Pirates with a thunderous shot from outside the box after combining with Lorch - with the Zambian opening his scoring account at the Soweto giants.
Ten-man Celtic tried to push for a late equalizing goal, but the Pirates defence looked solid in the dying minutes of the game and ultimately, the hosts emerged 2-1 winners on the night.
Despite the victory, Pirates remained second on the league standings - a point behind log leaders Mamelodi Sundowns, who beat Chippa United 2-0 at home on the night, while Celtic also remained ninth on the table.