Namibia, who are competing in their fourth finals, were yet to taste a Cup of Nations finals victory.
The southern African nation should have defeated their North African opponents by a more handsome margin but were let down by poor decision making.
Namibian winger Deon Hotto scored in the 88th minute to hand the Brave Warriors their shock victory while keeping up the sequence of surprise results that have dominated the opening days of the tournament in Ivory Coast.
Hotto snuck in at the back post to hand Namibia, a team placed 87 places below Tunisia in the FIFA world rankings, their deserved win as they were markedly more enterprising and created the better chances in the opening Group E encounter at the Amadou Gon Coulibaly Stadium.
Victory for the Namibians earned them their first three points at AFCON and first place in Group E.
The second group match will be played later on Tuesday between Mali and South Africa.
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