Chiefs thumped Black Leopards 4-0 in their last-16 clash to progress as Free State Stars knocked out last year's winners Orlando Pirates 2-1 after extra-time.
SuperSport just about edged United FC 1-0 with Cosmos beating Platinum Stars on penalties after the game had ended 1-1 after extra-time.
Meanwhile, Amazulu, who ousted Witbank Spurs 1-0 will clash with Santos with Mamelodi Sundowns drawn against Maritzburg United.
Santos defeated Roses United 1-0 in Cape Town with PSL league leaders Sundowns seeing off Wits 2-0.
And Maritzburg put an end to Golden Arrows' cup hopes with their 1-0 win.
Quarter-final draw in full:
SuperSport vs Jomo Cosmos
Kaizer Chiefs vs Free State Stars
Amazulu vs Santos
Mamelodi Sundowns vs Maritzburg United