A rare appearance for Jorry Matjila and Ryan De Jongh headlined Celtic's eleven, while Deon Hotto and Cole Alexander were recalled for Wits as Sifiso Hlanti dropped to the bench again.
Wits were given a dream start after Keegan Ritchie fired home from the penalty spot on three minutes after Celtic defender Wandisile Letlabika clipped Terrence Dzvukamanja in the area.
The lead came under threat right on 11 minutes after Wits goalkeeper Ricardo Goss was forced to go down to parry Ndumiso Mabena's free-kick before De Jongh hoofed the follow-up.
Goss kept Wits in the game following a point-blank save off Motebang Sera's close-range shot at the midway point after Siphelele Luthuli's first-time strike flashed the bottom-low post.
Wits finally gave in to the pressure nine minutes to halftime as Mabena picked the bottom corner with a penalty of his own, after he he was brought down under Lorenzo Gordinho's challenge.
A double substitution straight after halftime from the Clever Boys saw Mpho Mathebula and Mxolisi Macuphu introduced in place of Thabang Monare and Rowan Human.
The Clever Boys could've retaken the lead on 55 minutes with a cutback from the left-side spotting Mathebula, but Celtic shot-stoppr Sipho Chaine went down to pluck out the first-time attempt.
Celtic likewise had a golden chance to go ahead a little later, however Sera could not direct Luthuli's cross on target before Phathutshedzo Nange's volley had Chaine rooted on his line at the other end.
Wits searched for the winner late on after sending Janovane September on for his debut, but neither side was able to find the winning goal as Gavin Hunt's troops remain in fourth spot.
Celtic: Chaine, Letlabika, Mahashe, Luthuli, Mashikinya, Sera, Fikizolo, De Jongh, Matjila, Lingwati, Mabena
Wits: Goss, Ritchie, Gordinho, Hlatshwayo, Macheke, Alexander, Monare, Nange, Human, Hotto, Dzvukamanja
Subs: Mhlongo, Hlanti, Phillips, Mathebula, September, Domingo, Sekgota, Mlonyeni, Macuphu