Amazayoni secured the victory thanks to two goals by Clifford Mulenga, who has now scored three times in his last two matches for the club.
Usuthu, after this defeat, remain rock bottom of the table and the pressure will be growing on coach Neil Tovey.
Aces took the lead midway through the first half when former Bidvest Wits and Thanda Royal Zulu player Mulenga fired home a low shot from outside the penalty area.
On 33 minutes Amazayoni almost made it 2-0, with Lindokuhle Mbatha heading just over from Jacob Machaka's free-kick.
On 62 minutes Mulenga grabbed his second goal of the game, heading home a cross from Rudiger Gilbert. The Zambian capitalised on some poor marking in the heart of defence.
Mulenga looked to complete a hat-trick ten minutes later but fired his long-range effort wide, while Mtsweni’s free-kick was tipped over by Nicolas Gindre on 77 minutes.