Zimbabwean Macclive Phiri made his debut for the hosts, while Federic Nsabiyumva, Diamond Thopola, Elvis Moyo and Thabo Rakhale were among the changes for Chippa.
Eva Nga missed a clear chance to give the Clever Boys the lead as he headed wide of target following a corner kick inside the opening ten minutes.
A troubling shoulder injury however cut Eva Nga's evening short after 16 minutes and was replaced by Mxolisi Machupu.
The hosts still surged ahead following the 27th minute after Thulani Hlatshwayo got close to a corner kick before heading into the bottom near area via a deflection.
Two minutes later, Phathutshedzo Nange's long range drive took a bounce and hit the far corner to double their lead amidst a scrambling Veli Mothwa.
Thopola made way for Gregory Damons following the start of the second half, as Chippa attempted to get back into the overall contest.
A superb save from Mothwa five minutes after the break denied the Clever Boys a third after Thabang Monare unleashed from the edge of the danger area, before the Chilli Boys shot-stopper pulled off a double save off a free-kick from Elias Pelembe and Terrence Dzvukamanja on the follow up.
Nange should've completed his brace after the 63rd minute when he met a cross from the left, however the diminutive attacker headed wide of the far post.
Chippa struggled to carve out any openings, though had the home side on the edge amidst a few half-hearted scary moments around the area.
Nange went close to his second of the evening towards the final minutes, but Mothwa got down to palm the danger -granting Wits a quarter-final ticket.
Wits: Petersen; Mkhwanazi, Hlatshwayo, Gordinho, Phiri, Hotto, Monare, Nange, Pelembe, Dzvukamanja, Eva Nga.
Subs: Goss, Domingo, Hlanti, Alexander, Doutie, Macuphu, Sekgota.
Chippa: Mothwa, Modisane, Maziya, Thopola, Mayo, Nsabiyumva, Mahola, Komane, Jodwana, Rakhale, Kwem.
Subs: Mazibuko, Gamildien, Damons, Sekotlong, Twala, Sibeko, Makobela.