Mushangazhike scored the goals in both halves to down the Brave Warriors
Zimbabwe now top Group 2 with four points ahead of Namibia.
Meanwhile Kenya defeated Guinea 2-0 in Group 2 of the 2010 World Cup and Africa Cup of Nations qualifiers on Saturday.
France-based striker Dennis Oliech scored both goals for the home side in Nairobi.
The Auxerre ace gave Harambee Stars the lead after just three minutes with the second coming five minutes after the break.
The defeat is a severe blow to Guinea's aspiration of reaching the second phase of the qualifiers.
The Sylli National, who played at the recent African Cup of Nations in Ghana, were held to a 0-0 draw by Zimbabwe in Conakry last week.
The next round of matches will be played next week when Kenya host Zimbabwe while Namibia take on Guinea in Windhoek.
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