The Students had led 3-0 from the first leg and predictably coach Gavin Hunt fielded a weakened team for the return leg at the Somhlolo Stadium.
Leopards took the lead on 15 minutes through Muzi Dlamini, before Zweli Nxumalo made it 2-0 from the penalty spot on the hour-mark.
Mathokoza Twala then through levelled the aggregate score at 3-3 in the 71st minute, forcing the game to a penalty shootout where the hosts completed a remarkable turnaround with a 6-5 win, with Kabelo Paseka missing the decisive kick for Wits.