Played behind closed doors, the first opportunity fell to Bucs, with Justin Shonga heading glaringly off goal in the opening five minutes.
Augustine Mulenga found the outside post later on after running onto a through ball.
Soon, the home side eased the pressure and went ahead after Luvuyo Memela's scuffed shot was diverted into an empty net by Sifiso Hlanti on 13 minutes.
After struggling to get into the game, Bucs pushed for a second and Innocent Maela came close on 32 minutes but shot dismally off target.
The second goal duly came on 36 minutes following another defensive blunder as Hlanti played in Mulenga, who took his time to beat Kyle Peters at the near post with a low shot.
It got worse for the Students when Nazeer Allie conceded a penalty following a rash challenge on Mulenga.
Shonga stepped up to send Peters the wrong way for a three-goal cushion heading into the break.
Trailing by three goals, Wits made a double switch at the start of the second half in Lehlohonolo Majoro and Reeve Frosler.
THe visitors looked to sustain the early pressure in the second half following their change in personnel and gave a good account of themselves in that regard.
It was not enough to prevent Shonga from completing his brace, though after rounding Peters from a long ball from the middle.
Wits were looking for a consolation, and Majoro saw his shot cleared off the line after pouncing on an error by Siyabonga Mpontshane after 82 minutes.
The former Bucs man got another opportunity at goal, this time from 12-yards out from a penalty but Mpontshane made a blinding save to keep their clean sheet intact and march on with the maximum points.