A 73rd-minute strike by Arsenal forward Iwobi handed the Super Eagles a 1-0 success over Zambia in Uyo, ensuring top spot in Group B with a game to spare.
"It was my goal to qualify this team to an amazing tournament like the World Cup," said Nigeria captain Mikel Obi.
"I'm proud to captain this team of great players and coaches.
"My wife is Russian and she and the kids will be in Russia to cheer us at the World Cup."
Ghana, quarter-finalists at the 2010 World Cup in South Africa, were eliminated after managing only a goalless draw in Uganda when needing a win to keep their slim hopes alive.
It means Egypt can join Nigeria with victory at home to winless Congo on Sunday.
Failure to do so would mean Uganda can still pip them to top spot in Group E, with both facing away trips next month.
Uganda, who were promised $3,000-a-man to beat Ghana, created the better first-half chances in Kampala but William Kizito spurned the best of those.
South Africa recorded their first win in Group D with a 3-1 success against Burkina Faso despite losing Bongani Zungu to a red card in the second half for retaliation.
Bafana Bafana raced to a 3-0 first-half lead with a highly controversial Percy Tau goal, followed by strikes from Themba Zwani and Sibusiso Vilakazi.
Burkina Faso's consolation was a superb free-kick by Bertrand Traore three minutes from time.
Senegal top group D after late goals from Diafra Sakho and Cheikh N'Doye earned them a 2-0 win at Cape Verde.
Senegal have eight points with Burkina Faso and Cape Verde on six and South Africa on four.
Senegal and South Africa have an extra game left because they must replay a match originally won 2-1 by Bafana Bafana that was annulled over match manipulation by the Ghanaian referee.
DR Congo's 2-1 win in Libya ensured Group A will go down to the wire, although Tunisia need only a point at home to Libya to secure qualification after Youssef M'Sakni's hat- trick fired them to a 4-1 win at Guinea.
Ivory Coast dropped to second after drawing 0-0 in Mali on Friday but they host Morocco in a winner-takes-all clash next month.
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