A brace from star midfielder Sunday Mba helped Nigeria trounce nine-man Côte d'Ivoire 4-1 in Kaduna and virtually seal a place in the finals for the first time.
Morocco are equally well-placed to compete in South Africa next January after a 1-0 away win over Tunisia via a late Abdessamad Mbarki goal.
Mali, Senegal and Burkina Faso built leads at home in other matches while a Fifa ban forced Cameroon to cancel a fixture against Gabon.
The Nigerian Super Eagles are strongly positioned to progress in a competition restricted to footballers playing in their country of birth.
Coach Stephen Keshi took eight local stars to the Confederations Cup in Brazil last month and all were in the squad to face the Ivorians.
A home victory was expected in the northern city of Kaduna, but the margin must have thrilled even hard-to-please former national team captain Keshi.
Côte d'Ivoire did not help themselves by having Roger Assale and Baresi Gloudeaou sent off in the second half.
Nigeria's two-man advantage
However, Nigeria were already 3-1 ahead and scored only through Ifeanyi Benjamin when they had a two-man numerical advantage.
Star midfielder Sunday Mba once again punished Côte d'Ivoire by scoring in each half and Gambo Mohammed was the other Nigerian marksman.
Mba scored the winner when Nigeria eliminated pre-tournament favourites Côte d'Ivoire this year en route to winning the Africa Cup of Nations in South Africa.
Tiecoura Koulibaly was on target for the visitors just before the break to leave the Elephants trailing 2-1 at half-time.
Even the second-half red carding of Moroccans Mohamed Aberhoune and Salaheddine Essaidi could not prevent Tunisia losing in the Mediterranean resort of Sousse.
Seeking a first appearance at the finals, Morocco snatched victory in the final minute when Mbarki finished off a swift counterattack.
Goalkeeper Farouk Ben Mustapha was the lone survivor from the Tunisian team that trounced Angola 3-0 to win the 2011 final in Sudan.
While most second legs are scheduled for the end of July, the Maghreb rivals meet again next weekend in coastal city Tangier.
Mali overcome Guinea
Mali came from behind to overcome Guinea 3-1 in Bamako through goals from Moussa Kone, Cheick Doumbia and Drissa Traoré.
Guinea, who squeezed past Sierra Leone on away goals in the preliminary round, went ahead on eight minutes through Sambegou Bangoura.
Yannick Gomis scored nine minutes after half-time to give favoured Senegal a 1-0 victory over minnows Mauritania in Dakar.
The Mauritanians beat Liberia home and away to reach the first round and are trying to reach the finals of a Confederation of African Football competition for the first time.
A solitary goal also settled the match between Burkina Faso and Niger in Ouagadougou with substitute Issouf Kabore scoring for the home side.
Fifa banned Cameroon this week over state meddling in the running of football, leading to the cancellation of the fixture with Gabon in Yaounde.
Hosts South Africa are automatic participants in the 2014 tournament and will be joined by 15 nations after region-based qualifiers. – AFP