Lucas Ribeiro Costa converted the lone penalty in the 21st minute, joining Khanyusa Mayo as the league's top scorer with seven goals.
Despite AmaZulu's spirited efforts, a 65th-minute goal by Hendrick Ekstein was controversially disallowed for offside.
AmaZulu played without captain Veli Mothwa, and the fixture was relocated from Moses Mabhida Stadium due to pitch repairs and upcoming events.
Sundowns, previously winless in their last three Durban visits, displayed dominance, controlling the game and frustrating Usuthu's attempts to break through.
The match had its fiery moments, with tensions boiling on both benches. Sundowns coach Rulani Mokwena faced perceived unjust criticism in the media.
The first half showcased Sundowns' superiority, with Costa's penalty and a crucial save by Olwethu Mzimela from Peter Shalulile.
AmaZulu saw glimmers of opportunity before half-time, but Ronwen Williams' composed goalkeeping denied their attempts.
The second half witnessed an improved AmaZulu performance, but Sundowns' defence held firm. Despite Usuthu's persistent efforts, Ekstein's flagged offside goal added to their frustrations.
Sundowns secured another victory, maintaining their impressive start to the season.