Four goals from Klate and two own goals handed The Clever Boys an emphatic victory tp ensure their passage into the Nedbank Cup quarter-finals.
The former Orlando Pirates attacker opened the scoring in the 21st minute with a well-hit half-volley to steer home a cross from Siyabonga Nhlapo.
Two minutes later the visitors had their lead fortuitously doubled thanks to Oupa Seete, who accidentally turned home another Nhlapo cross from the right flank.
Klate then completed his hatrick in the final five minutes of the first half as he banged home with his right foot from close range before coolly slotting home a 45th minute penalty.
It was a big ask for Magesi to fight back from 4-0 down at half-time, however, the hosts put up a fight for much of the second half as they wasted a couple of opportunities in front of goal.
It went from bad to worse for the Polokwane-based side in the 81st minute as goalkeeper Rendani Maduwa turned home Sibusiso Vilakazi's low shot after a failed attempt at a save.
Less than a minute later, Klate added a final nail to the coffin as Wits booked their place in the Nedbank Cup quarter-finals.
Magesi: Maduwa, Makhwe, M Baloyi (Moloto 65'), Selabe, Seete, Moremi, Ndlovu (Moses 48'), Nhlabathi, Morakaladi, Mahlakoane, K Baloyi
Wits: Josephs, Hlanti, Allie, Khumalo, Nhlapo, Motshwari (Sekese 74'), Klate, Vilakazi, Shongwe (Sheppard 60'), Pelembe (Mosiatlhaga 62'), Keene