Haashim Domingo opened the scoring at the Moses Mabhida Stadium on 16 minutes, and Gaston Sirino extended the Citizens' lead minutes after the half-time break.
Sebastien Roussety reduced the deficit with 53 minutes played but Tashreeq Morris scored from penalty spot in stoppage time to secure the result.
City had earned their second-round place after beating Rukinzo 3-1 over two legs as Port Louis knocked out Jwaneng Galaxy.
The two teams face off in the second leg on Sunday, 25 October at the National Sports Complex.
Durban City coach Eric Tinkler has challenged his players to improve their finishing after their 3-1 victory over AS Port Louis 2000 in the first leg of the CAF Confederation Cup second preliminary round on Sunday.
Kaizer Chiefs coach Fernando Da Cruz remains convinced that his side can turn their CAF Confederation Cup campaign around despite suffering a narrow defeat to Red Arrows.
Kaizer Chiefs coach Fernando da Cruz is confident his side will overturn their 1-0 CAF Confederation Cup Second preliminary round deficit against Red Arrows.
Red Arrows coach Chisi Mbewe was delighted to steer his side to a 1-0 victory against Kaizer Chiefs in their CAF Confederation Cup Second qualifying round first leg clash.
