Gabon struck the woodwork in the first half of their match in the Mozambican capital, but were under pressure for most of the game.
Zambia moved a step closer to the next round with a precious away win as Winston Kalengo scored in the 28th minute in the provincial town of Karima, on the banks of the River Nile.
Both ties are finely poised ahead of this weekend's return legs, with Mozambique travelling to Gabon on Saturday and Zambia hosting Sudan in Ndola on Sunday.
The two matches kicked off six days of second round qualifiers across the continent that will leave 20 countries to compete in the final group phase next year.
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(Reporting by Mark Gleeson in Cape Town; Editing by Toby Davis)
