Joel Mogorosi and Ruzaigh Gamildien netted in the first half before Lerato Manzini made it three in the second.
In the opening minutes Gamildien hit a shot wide and missed a header, before Manzini missed a headed chance as well, as Celtic had the better of the opening exchanges.
Then, in the 23rd minute, after some not-so-clever defending from Wits, Mogorosi was left unmarked on the right, and with plenty of space calmly passed the ball through Ryan Harrison’s legs.
Phunya Sele Sele then doubled their lead when Gamildien finally connected with a header, after a cross from Tsietsi Mahoa on the left wing, hitting the bottom left corner.
Wits had the chance to reduce the deficit on 50 minutes, when substitute Matthew Pattison went on a solo run, but with only the keeper left to beat he poked the ball into the side netting.
Celtic made it 3-0 just past the hour mark, when Manzini received a cross from the left and powered home from the far post.