Iwobi struck with 17 minutes remaining of the match at the Godswill Akpabio International Stadium in Uyo as Nigeria reached the World Cup for the sixth time.
The result gives Nigeria 13 points from five games in Group B, with Zambia, their nearest challengers, on seven points with one game to play.
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The Super Eagles have now qualified for seven of eight World Cups, the only exception since their debut in 1994 being Germany 2006.
Ghana, however, are all but eliminated after a 0-0 draw against Uganda which witnessed huge controversy as a last-gasp goal was wrongly ruled out for offside.
Egypt will qualify from Group E if they beat Congo on Sunday - they have not played at the World Cup since 1990.
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