The Buccaneers welcomed back Luvuyo Memela from injury after he missed the midweek Nedbank Cup loss to Cape Town City while Milutin Sredojevic made two changes from Wednesday’s encounter.
Arrows, who ended Bucs' top-eight hopes in the final game last season, were quickly on the backfoot when Memela tried to whip his way to the box, but Limbikani Mzava was on high alert.
The high-pressured game continued when Xola Mlambo looked to round off a well-orchestrated move with a goal, but he was unable to beat Maximilian Mbaeva who came up with an easy save on 15 minutes.
The visitors appealed for a penalty minutes later after Justin Shonga left the Arrows defence in their wake only to be hurled down by Siyabonga Dube with the match officials waving the appeal away.
Memela looked to pull clear with the opener with a shot from outside the box, but the winger blasted tamely at Mbaeva as the first half ended goalless.
Pirates wasted no time going in front four minutes into the second half after Musa Nyatama set up Thembinkosi Lorch for an exquisite finish from the right side after Arrows was caught napping.
In the 55th minute, referee Thando Ndzandzeka mistakenly handed a second yellow and red card to Limbikani Mzava for a foul on Memela, with TV replays showing he did not commit the crime.
Clinton Larsen made two substitutions in Jabulani Shongwe and Wayde Jooste, having to rally back with a man short.
On the other hand, Bucs increased their lead after Mthokozisi Dube got in on the blind side to force the all-important second after a clearance from Arrows went wrong.
Former Arrows striker Thamsanqa Gabuza replaced Shonga minutes to the end, with Pirates cruising on course for the maximum points.
Shongwe pulled a goal back for the hosts after a poor clearance as he blasted into the roof of the net to set up a nervy closing few minutes for the Bucs faithful.
The Sea Robbers were quickly looking to regain the two-goal deficit with Nyatama racing through goal, but he found Mbaeva, who managed to block the goal-bound effort.
Despite the late pressure, the Soweto giants held on for all three points to reduce the gap to one point between themselves and Sundowns.