January signing Ivan Mahangwahaya made his Baroka debut as did Denis Chembezi, who accompanied Cyril Chibwe and Sicelokuhle Hlatshwayo at the back for Rise and Shine.
Baroka, who won the two league fixtures against City this season, were under pressure earlier on as Mohammed Anas forced Elvis Chipezeze to a save, with Denwin Farmer nearly netting an own-goal moments later.
Walter Musona had the chance to give City the lead inside 18 minutes though after working his way into the area, fired straight at Chipezeze amidst defensive pressure.
Rise and Shine's earlier momentum dropped towards the end of the half, as Bakgaga began venturing into advanced territories.
After a somewhat disappointing first half, City shuffled their stall at the start of the second half as Anas made way for Charlton Mashumba in the final third.
The away side started the second stanza more promising than the first as Tshediso Patjie flashed wide from the right after a ball from Goodman Mosele 60 minutes gone.
Dylan Kerr put on an offensive change three minutes later in Prince Nxumalo as the visitors looked for the opener whilst Thamsanqa Masiya made way.
Chibwe tipped Mosele's long-range drive for a corner after the71st minute with Bakgaga Ba Ga Mphahlele searching for the breakthrough. From the corner, Nxumalo got in on the near side to turn home the opener from point-blank range with the defence caught wanting.
Rise and Shine went all out in search of the equaliser to force the match into extra time, but were unable to breach Chipezeze's goal as Bakgaga advanced to the last 16 for a date with Hungry Lions.
Polokwane: Chibwe, Semenya, Hlongwane, Chembezi, Hlatshwayo, Chauke, Musona, Nene, Anas, Tlolane, Booi.
Subs: Phali, Phiri, J. Maluleke, Mahlasela, W. Maluleke, Mashumba, Hlubi.
Baroka: Chipezeze, Farmer, Patjie, Kambala, Sampson, Phiri Jnr, Mosele, Mahangwahaya, Ngubane, Gerbhardt, Masiya.
Subs: Dlamini, Maloka, Nxumalo, Madondo, Makume, Khwinana, Mbulu.