Cameroon goalkeeper Charles Itandje (Photo: AP)
Given a second chance after Cape Verde were disqualified, the Tunisians attacked relentlessly in the early stages only to be foiled by the 30-year-old France-born shot-stopper.
Cameroon captain Samuel Eto'o, back after a short-lived retirement, was always a threat in the first leg of a tie offering a ticket to the 2014 finals in Brazil.
The teams, who boast 10 World Cup appearances between them, clash again in the second leg in Yaounde on November 17 with the odds favouring the 'Indomitable Lions'.
Tunisia flew out of the starting blocks with Amine Chermiti having a shot blocked by Itandje with just 10 seconds gone at Stade Olympique on the outskirts of Tunis.
Houcine Ragued and Chermiti again went close as the 'Carthage Eagles' sought an early breakthrough while Eto'o saw his long-range shot comfortably saved at the other end.
Itandje had to be at his acrobatic best on 17 minutes, pushing over a dipping medium-range drive from Wissem Ben Yahia.
There was no rest for the Cameroon shot-stopper, this time keeping out a Chermiti header as Tunisia used the flanks to create chances.
Eto'o was the victim of a two-foot lunge from behind by Sameh Derbaly and recovered to later cut the ball back for Jean Makoun, who should have done better than fire wide.
Substitute Ben Fakhreddine Youssef and Pierre Webo squandered good chances in a less frenetic second half.
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