Earlier on Friday, Ghana scored in the 85th minute to earn a 1-1 draw against visiting Congo in Group E.
Odion Ighalo, John Mikel Obi, Victor Moses and Kelechi Iheanacho were all on target for Nigeria in their victory.
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The win means the Super Eagles top Group B on nine points while Cameroon have just two after three matches.
Zambia and Algeria both have a point each and they play their third match, against one another, on Saturday in Lusaka.
Nigeria took the lead on 29 minutes when Ighalo latched onto a ball over the top from captain John Mikel Obi before drilling home.
Ighalo was then booked for revealing a T-shirt in support of his international colleague Carl Ikeme, who is suffering from leukaemia.
Just before half-time, a corner from Moses was turned in by his former Chelsea team-mate Mikel Obi as he stabbed into the roof of the net from close range.
Moses scored the third in the 55th minute after an exchange of passes with Moses Simon.
The rout for Cameroon, who won the Africa Cup of Nations in February, was completed when Leicester City striker Kelechi Iheanacho stooped to head home a cross from Ogenyi Onazi with 14 minutes left.
2018 World Cup qualifiers for Africa (rounds 3 and 4)
Thursday: Monday:
Uganda 1-0 Egypt (Grp E) Cameroon v Nigeria (Grp B)
Guinea 3-2 Libya (Grp A) Libya v Guinea (Grp A in Tunisia)
Friday: Tuesday:
Ghana 1-1 Congo (Grp E) Congo v Ghana (Grp E)
Nigeria 4-0 Cameroon (Grp B) South Africa v Cape Verde (Grp D)
Cape Verde v South Africa (Grp D) Ivory Coast v Gabon (Grp C)
Morocco v Mali (Grp C) DR Congo v Tunisia (Grp A)
Tunisia v DR Congo (Grp A) Burkina Faso v Senegal (Grp D)
Saturday: Egypt v Uganda (Grp E)
Zambia v Algeria (Grp B) Mali v Morocco (Grp C)
Gabon v Ivory Coast (Grp C) Algeria v Zambia (Grp B)
Senegal v Burkina Faso (Grp D)
In Kumasi, Ghana's World Cup chances suffered a severe knock and despite dominating large parts of the match, it was Congo who opened the scoring goal after 18 minutes through Thievy Bifouma.
Black Stars defender Joseph Attamah had a debut to forget as he was dispossessed on the edge of the area by Fabrice Ondama, who cut the ball back for Bifouma to score.
One of Ghana's best efforts in the first half came from Atletico Madrid's Thomas Partey who forced a good save by Congo goalkeeper Barel Mouko from a long-range effort.
It took until five minutes from time for Partey to equalise with his first international goal.
He scored with a low angled shot across Mouko after a superb pass from Newcastle United's Christian Atsu just outside the area.
The result means Ghana stay third in Group E with just two points from three matches, while it was a first point of the campaign for Congo.
Uganda are top of the group on seven points after yesterday's 1-0 win over Egypt, who are second on six points.