Leopards coach Dylan Kerr kept faith with the same eleven from the abandoned match, while Granwald Scott, Deon Hotto, Elias Pelembe, Gift Motupa and Simon Murray came in for Wits.
Wits' nervous start needed the saving grace of Ricardo Goss to keep out Marks Munyai’s close-range shot on 18 minutes.
Exactly ten minutes to halftime, Leopards fell behind when Motupa cushioned home a cross Pelembe as the Leopards defence went to sleep.
Murray closed in on a second two minutes later, but he sent his header wide of the post following a cross from Vuyo Mere.
Upon resumption on the second half, Wits looked to increase the tally when Murray flashed a header just wide of the far post off Pelembe’s supply on 52 minutes.
With a quarter of the match remaining, Gavin Hunt looked to shore up the match with the substitution of Keegan Ritchie for Motupa.
However, the Limpopo side equalised ten minutes to the full-time whistle when Mwape Musonda rose high to head past Goss, sending the match to extra time.
The two sides failed to invigorate the encounter in either half, with Musonda missing a sitter at the end as penalties decided the winners.
Following two misses apiece, Kapinga’s dismal effort over the crossbar saw Wits march to the last eight ahead of Thursday's draw.
Leopards: Muleka, Munyai, Mashoene, Munganga, Ndou, Masalesa, Ngambi, Kapinga, Musonda, Mhlongo, Sekotlong.
Subs: K. Ndlovu, K. Masia, Mokoena, Hlongwane, Tshepe, T.Ndlovu, X. Ndlovu.
Wits: Goss, Mere, Hlatshwayo, Johannes, Hlanti, Scott, Alexander, Hotto, Pelembe, Motupa, Murray.
Subs: Keet, Nonyane, Ritchie, Kumalo, Mhango, Lakay, Majoro.