The Wits goals were scored by Sifiso Vilakazi, Marawaan Bantam and Tefu Mashamaite while Songwe Chalwe and Siphamandla Zak scored for lions.
The PSL side surrendered a two goal cushion to their never say die opponents and eventually prevailed when their captain Mashamaite found the winner during the first period of extra-time.
Wits hit the front just past the half hour mark, completely against the run of play.
Striker Sifiso Vilakazi capitalised on some hesitancy in the Lions defence. He snuck in between two defenders and prodded home.
Bantam increased the visitors lead two minutes later when he dribbled his way past Lions defender Nhlanhla Mncube and fired past Mponsthana.
The home side got back into the contest with a sweeping move that was eventually finished off by Songwe Chalwe who netted with a crisp header.
Lions upped their efforts in the second half and should have drawn level in the 55th minute when Zaca, who came on at the start of the second half, missed a tap in.
The home side spurned another chance to even matters when Mncube missed from the penalty spot.
Zaca atoned for his earlier miss by dispossessing a Wits defender and slotting past keeper Francis Chansa in the 73rd minute.
Thando Mngomeni had a chance to seal it for Wits, with two minutes of regulation time remaining, but he directed a volley from Calvin Kadi’s cross onto the Lions upright.
Mashamaite powered a header home from Sipho Mngomezulu’s cross in the 104th minute, to send the visitors into the next round.
Lions: (4-4-2) Mpontshana; Dlamuka, Konan, Mncube, Mkhwanazi; Gomoshe (Gcaba 81’), Kubheka, Wiltwer, Makhoba (Dlamini 99’); Chalwe, Makhanya (Zaca 46’)
Wits: (4-5-1) Chansa; Mngomezulu, Batabaire, Mashamaite, Phungwayo; Myeni, Radebe, Haskins (Sibande 73’), Bantam, Tshabangu (Kadi 65’); Sif. Vilikazi (Mngomeni 74’)