Thabang Monare opened the scoring five minutes into the opening half, heading home his second goal of the season after latching onto Elias Pelembe’s well placed free-kick.
Celtic drew level on the half hour mark through Atusaye Nyondo, his first time effort skidding into the bottom corner after neat interplay between Nyatama and Lakay.
The sides went into the break deadlocked at 1-1 with both sides playing positive football.
Former Bloemfontein Celtic striker Gabadinho Mhango handed the lead back to Gavin Hunt’s men five minutes after the restart, picking up a loose ball on the edge of the area and slotting his effort beyond Tignyemb.
Bidvest Wits looked disciplined at the back and controlled the midfield to see out the remainder of the match as Celtic look to hit on the counter.