Nathan Paulse slotted a 24th minute penalty - after Siyabonga Nhlapo was sent off for clattering Toriq Losper in the box - to give the Urban Warriors a 2-1 victory on aggregate.
Chiefs defeated Bloemfontein Celtic by the same scoreline at FNB Stadium on Saturday.
The Students started the game stronger, with Elias Pelembe shooting straight at Anssi Jaakkola early on following a cross from the left by fellow new signing Daine Klate.
Wits, however, were knocked back when Nhlapo was shown a straight red card midway through the first stanza. Nhlapo brought down Losper following a brilliant flick-on by Paulse, who converted the resultant spot-kick.
The hosts suffered a further setback in the 37th minute, as veteran forward Henrico Botes sustained an injury, prompting the introduction of Portuguese recruit Joaquim Lupeta.
Lupeta almost made an immediate impact, but he fired wide from close range a second after appealing for a penalty for a hand-ball in the box by Paulse.
The Urban Warriors piled on the pressure in the second half, with Paulse in particular a constant menace.
However, Moeneeb Josephs made a number of fine saves, notably denying Cecil Lolo from the spot in the 86th minute after Ben Motshwari fouled Losper.