Usuthu defeated fellow top-flight side Polokwane City 2-1 after extra-time, while Milford needed penalties to see off third-tier debutants Soweto Super United M17 following a 1-1 draw.
The draw for the Last 16 will take place on Wednesday from 19h00.
AmaZulu took a 10th-minute lead at the Old Peter Mokaba Stadium when defender Taariq Fielies found the back of the net, his second career goal in the Nedbank Cup.
Polokwane were reduced to 10 men when Monty Batlhabane received a straight red card for a dangerous tackle on Usuthu’s Liam Bern, the first red card of the 20-year-old’s career.
City levelled before halftime as Lebohang Nkaki converted a penalty after Riaan Hanamub fouled Thabang Matuludi in the box.
The match went to extra-time, and it was AmaZulu who grabbed the winner as Nkosikhona Radebe’s shot from outside the box was turned in by Zimbabwean forward Thandolwenkosi Ngwenya, who scored his seventh goal of his debut season in South Africa.
Milford were given a major scare by ABC Motsepe League outfit SSU M17 at the Dobsonville Stadium.
Milford took the lead just past the half-hour mark when Sifiso Mdluli found the back of the net, but the hosts were level before halftime.
Thapelo Tshilo scored for the amateur side, much to the delight of the partisan crowd in Dobsonville.
The sides could not be separated after 90 minutes, sending the match to extra-time, during which SSU M17 were reduced to 10 men when former Venda and JDR Stars defender Chris Matombo received a second yellow card.
The tie was eventually settled by penalties, with Milford holding their nerve to book a place in the Last 16.