The entertaining match had ended in a 2-2 stalemate after regulation time and extra-time.
As a result, Rise and Shine progress into the semi-finals, while the Buccaneers, who won the league cup in 2011, bow out of this year's competition.
Bucs were eager to return to winning ways after succumbing to a 3-1 defeat to Mamelodi Sundowns in a PSL encounter at home on Wednesday night - having edged out Lamontville Golden Arrows 1-0 in a Last 16 match in Durban a week ago.
Milutin Sredojevic made four changes to the starting line-up that faced the Brazilians. Ntsikelelo Nyauza, Musa Nyatama, Justin Shonga and Thamsanqa Gabuza made their return to the Bucs starting line-up.
Rise and Shine were oozing with confidence after holding an in-form Kaizer Chiefs side to a 0-0 draw in a league match in Polokwane. Polokwane defeated Ajax Cape Town 4-3 on penalties in a Last 16 match at home a week ago and they advanced to the last eight.
The hosts conceded early for the second successive match after their defence was caught napping and it was Rendani Ndou, who punished the Buccaneers.
The 30-year-old marksman headed past Pirates goalkeeper Sandilands to make it 1-0 to Polokwane with Rodney Ramagalela grabbing an assist.
This was Ndou's second goal of the season - having also netted against Pirates in a league match two months ago and Bucs had to find a way to level matters.
The Buccaneers applied some pressure on the Rise and Shine defence and the visitors were forced to defend too deep.
Parity was restored after the visitors made a mistake on the edge of the box and Nyauza pounced. The defender fired past Polokwane keeper George Chigova to make it 1-1.
Pirates were then awarded a penalty after Chigova was adjudged to have fouled Gabuza in the box and the referee pointed to the spot-kick.
But the Zimbabwean made amends as he produced a fine save to deny Mpho Makola from the spot-kick, but Chigova injured himself in the process and he was replaced by Harold Ndlovu.
The hosts continued to dominate, but Rise and Shine managed to restore their lead against the run of play and it was Ndou, who made it 2-1 to Polokwane.
However, Sredojevic's men never lost hope as they equalized again through Makola's header from close range - ensuring that the first half ended with the two sides locked at 2-2.
Pirates dominated the early stages of the second half with the Polokwane defence struggling to contain the home side's speedy wingers Qalinge and Lorch.
The hosts were denied a legitimate penalty when dribbling wizard Lorch was fouled by Sammy Seabi inside the Polokwane box, but the match referee Victor Gomes waved play on.
Walter Maponyane, the former Sundowns defender, looked solid at the heart of the Rise and Shine defence as they continued to absorb pressure from Bucs.
The Soweto giants were forced to try their luck from range with Marc van Heerden's thunderous' effort narrowly missing the target in the closing stages of the match.
The game went into extra-time as it ended in a 2-2 draw in regulation time. Sandilands and Ndlovu were not beaten in extra-time and a penalty shootout followed.
Pirates defenders Van Heerden and Nyauza missed their spot-kicks and Polokwane emerged 4-2 winners on penalties.