The two sides got off to a frantic pace, with Wits having to do loads of tackling in a bid to keep the hosts at bay.
Reserve goalkeeper Kyle Peters made an important block from preventing them from falling behind with the home side gunning for the early opener.
They kept piling on the pressure towards half-time as the Students had to keep defending, although they did hold their own against shots piling in from all angles.
Peters continued to be under siege when he had to pull off two good saves from well-executed attempts, while they struggled to get control into the game.
Pressure continued mounting for the visitors at the start of the second half, with Agosto continuing their search for the opening strike.
Wits,, though, looked more settled and went about their business after 58 minutes when Reeve Frosler picked out Thobani Mncwango but he directed his header off target.
Midfielder Daylon Claasen unleashed a shot from range, but it went wide, while Mncwango was unable to finish off Eleazar Rodgers' delivery across the face of goal delivery a minute later.
Rodgers looked dangerous as he picked out substitute Sifiso Myeni at the far post, who failed to finish off the inviting opportunity.
They went behind after 78 minutes with the hosts finishing off at the back post amidst the best efforts of a sliding Peters to secure a healthy advantage for the return-leg next weekend.
Wits: Peters, Hlatshwayo, Gyimah, Scott, Rodgers, Hlanti, Claasen, Mkhwanazi, Mncwango, Frosler, Majoro.
Subs: Keet, Khumalo, Ntshangase, Pelembe, Myeni, Kodisang.