City coach Benni McCarthy handed starts to new signings Peter Leeuwenbergh and Riyaad Norodien, with the latter donning the number 17 jersey.
It was Leeuwenbergh who was called upon after just three minutes as the Dutch shot-stopper produced a good save to keep out Khama Billiat's free-kick.
City had a chance of their own on 18 minutes as former Chiefs forward Matthew Rusike headed wide from Edmilson Dove's cross.
Other than a save from Itumeleng Khune to deny Thabo Nodada after 26 minutes, the final stages of the first half proved to be a quiet affair.
Former Chiefs striker Siphelele Mthembu went close to putting City ahead shortly after the break but his stinging effort was parried away by Khune.
The deadlock was eventually broken shortly after the hour mark with Martin slotting home from close range.
Leeuwenberg proved to be the busier of the two goalkeepers and he was called upon once again in the 76th minute to deny Bernard Parker an equaliser at the near post.
The Soweto giants threw numbers forward in search of a way back but the Mother City outfit managed to hold out in the closing stages to claim the win.
Chiefs: Khune, Mirwa, Cardoso, Mathoho, Moleko, Katsande, Meyiwa, Tshabalala, Parker, Billiat, Castro.
City: Leeuwenbergh, Mkhize, Fielies, Mngonyama, Edmilson, Putsche, Patosi, Nodada, Martin, Norodien, Rusike.
Subs: Stephens, Kouassi, Cupido, Seedat, Modise, Links, Kateregga, Matsi, Mthembu.