Joris Delle made a surprise appearance in the Sea Robbers goal ahead of Wayne Sandilands, with Siphelele Ndlovu and Zakhele Lepasa also giving a run. For Wits, Lorenzo Gordinho was finally handed his debut after joining from Kaizer Chiefs last month.
Pirates were put on the back-foot four minutes from kick off when Deon Hotto got behind Ntsikelelo Nyauza to run onto a flick on by Eva Nga but the Namibian was unable to find the target.
Furthermore, the Buccaneers were forced into a 12th-minute substitution after injury to Abel Mabaso saw Alfred Ndengane slotted in at the back.
The Buccaneers were behind on 28 minutes when Eva Nga fired home from the penaltu spot after Fortune Makaringe was ajudged to handled in the danger area.
Pirates searched for the equaliser later on, but the Clever Boys extended their lead just before halftime when Hotto beat Ndlovu for possession to drill into the far corner.
The Buccaneers turned to the bench following halftime and introduced Kabelo Dlamini who replaced Ndlovu but Wits went close to a third five minutes into the second half, but Nga headed against the foot of the post following an inswinging corner.
The Buccaneers finally halved the tally as Thembinkosi Lorch beat Gordinho to possession drill into the far corner 68 minutes in.
The Buccaneers were level 15 minutes from time when a free-kick from Luvuyo Memela found Happy Jele, who got in front of Goss to head home and ultimately sent the game to extra-time.
Wits finished with a man down after Elias Pelembe received a second yellow for questioning the referee's decisions on 105 minutes after Pirates were awarded a penalty, which Lepasa converted after Memela were brought dowm.
The Clever Boys almost fell further behind in the second period, but Goss denied Justin Shonga from close-range while Thulani Hlatshwayo threatened the equaliser at the other end.
The match went to a penalty shoot-out after Gift Motupa got goal-side to fire home the equaliser in the dying seconds of extra-time.
Nevertheless, Gordinho sent the Clever Boys into the last 16 with the final kick in the shoot-out after Pirates missed three of their kicks.
Pirates: Delle, Maela, Jele, Nyauza, Pule, Ndlovu, Makaringe, Mabaso, Lepasa, Memela, Lorch
Subs: Mpontshane, Ndengane, Mako, Mntambo, Dlamini, Shonga, Muwowo.
Wits: Goss; Hlanti, Gordinho, Mkhwanazi, Hlatshwayo, Monare, Nange, Domingo, Hotto, Sekgota, Eva Nga.
Subs: Petersen, Nonyane, Pelembe, Alexander, Doutie, Motupa, Dzvukamanja.