As a result, Bucs move to the top of the league standings, while Bakgaga climb to eighth spot.
Pirates head coach Milutin Sredojevic made only one change to the starting line-up that faced Chippa United in their maiden 2017/18 PSL match at the Orlando Stadium on Saturday.
Luvuyo Memela, a winger, replaced central midfielder Thamsanqa Sangweni, who is out nursing a knee injury which he sustained during Bucs' 1-0 victory over the Chilli Boys.
Baroka head coach Kgoloko Thobejane fielded a strong starting line-up which included Gift Motupa, who on a season-long loan deal from Pirates.
Former Kaizer Chiefs striker Lewis Macha, who had started for Bakgaga against Polokwane City in the Limpopo Derby which ended in a goalless draw on Saturday, was dropped.
The Buccaneers enjoyed possession in the final third in the opening stages of the match as they looked to penetrate the Bakgaka defence which was marshalled by Mzwanele Mahashe.
Bakgaga were forced to make an early change when Matome Kgoetyane went down injured and he was replaced by fellow defender Mathari Mothupa.
Innocent Maela, who was named the man of the match against Chippa, played a good cross into the Baroka box, but his Pirates teammate Thamsanqa Gabuza could not connect with the ball and it was cleared away.
The home side then had a chance to break the deadlock from a free-kick in a promising area a few minutes before the half-hour mark, but the Pirates wall did well to block Baroka winger Mpho Kgaswane's effort from the set-piece.
It was the visitors, who took the lead just before the half-time break when Mpho Makola set-up Thabo Qalinge in the blind spot and the latter beat Baroka goalkeeper Virgil Vries to make it 1-0 to Pirates.
The momentum was with Bucs as the interval approached and Memela set up Gabuza, who placed his header wide of the target, following a quick counter-attack.
The score was 1-0 to Pirates at half-time with the visitors having dominated the first half.
Bakgaga did most of the attacking in the early stages of the second-half, but new Pirates captain Thabo Matlaba and troops were solid at the back with goalkeeper Wayne Sandilands untroubled.
Sredojevic reacted by pulling out Memela, who was no longer making good forward runs, and he introduced fan-favourite Thabo Rakhale as the Buccaneers looked to regain full control of the match.
The Soweto giants nearly then doubled their lead when Qalinge combined with Gabuza, but the latter fired straight at Baroka shot-stopper Vries, who made a comfortable save.
Moments later, Pirates were made to rue that missed opportunity as Hassan Abdi Banda headed home from a corner-kick to make it 1-1 for Baroka after the Bucs defence was caught napping in the closing stages of the game.
Strikers Ayanda Nkosi and Thabiso Kutumela were then introduced by Sredojevic, but the Baroka defence stood firm and ultimately, the match ended in a 1-1 stalemate.