Shane Roberts and Zukile Kewuti were handed starts for the visitors, while Nana Akosah-Bempah led the attack.
There was not much to write home about in the opening 45 minutes for the Cape Town side, who were without head coach Benni McCarthy.
However, City managed to secure a vital away goal after the hour mark with Sibusiso Masina getting his name on the scoresheet.
The visitors remained resolute for the remainer of the contest to ensure they left Mozambique with a victory and a clean sheet.
City: 32. Stephens, 4. Kobola, 3. Mngonyama, 16. Johannes (c), 6. Seedat, 29. Roberts, 28. Kewuti, 10. Patosi, 24. Masina, 30. Martin, 14. Nana.
Subs: 1. Walters, 5. Edmilson, 27. Gumede, 7. Lakay, 21. Ralani, 26. Nodada, 20. Moseamedi.