Bukasa Kasonga deflected a cross from Patrick Phungwayo into his own net under pressure from Sibusiso Vilakazi on 17 minutes.
For the Clever Boys it is a significant result, marking the first time that they have reached the quarter-finals of the Telkom Knockout since its inception in 2006.
As for Usuthu, it is a second defeat at the hands of Wits in a matter of weeks, having been beaten 3-1 by the Johannesburg team in a League game under over a month ago.
Wits settled the quicker of the two teams, and the goal gave them the confidence to dominate the rest of the half – they should have gone into the break more than just 1-0 up.
Derrick Spencer and Ryan Chapman both missed put on glaring opportunities to add to Wits' advantage, and youngster Bhongolwethu Jayiya was unlucky not to double the home side's lead just before half-time, hitting the upright with a fearsome left-footed drive that had goalkeeper Mbongeni Mzimela beaten.
Usuthu upped their game in the second half and came close to an equaliser on the hour mark, with substitute Goodman Dlamini firing a shot just over the crossbar with one of his first touches after coming off the bench.
Dlamini had an even better chance a few minutes later, playing a one-two with Stanton Lewis before finding himself with only Energy Murambadoro to beat, but the goalkeeper came off his line quickly and did well to block the attacker's shot.
That proved to be the Durban team's last genuine scoring opportunity and Wits were able to hold onto their slender lead and secure a place in the last eight of the cup competition.