Mangoua Kesse broke the Abidjan deadlock on 34 minutes and second-half goals from Irenee N'Doua, Adama Bakayoko and Nigerian Olarenwaju Kayode completed an unexpectedly comfortable fourth round, first leg victory.
Regular African football campaigners Primeiro had come to the Ivorian commercial capital with a reputation embellished by a victory over title holders FUS Rabat of Morocco in the previous round. Portuguese coach Carlos Manuel boasted after that triumph that his team were capable of winning the second-tier African competition, but it is difficult to imagine ASEC surrendering a commanding lead.
Post presidential-election violence in Ivory Coast forced ASEC to play Motor Action of Zimbabwe and Raja Casablanca of Morocco away in single-leg CAF Champions League ties. Both matches went to a penalty shootout with the youthful team coached by Frenchman Sebastien Desabre won in Harare and lost in Casablanca - a defeat that meant demotion to the Confederation Cup.
Southern defeats for Moroccans
Angolan football followers still had cause for celebration as InterClube took a 3-0 lead over Difaa al-Jadida of Morocco in Luanda with Dias Caires and Moco grabbing late goals after Minguito scored on the stroke of half-time.
Moghreb Fes of Morocco also lost in southern Africa, but a 1-0 defeat by ZESCO United of Zambia in Ndola keeps alive hopes of qualifying for the eight-club group phase. Derrick Kabwe scored the winner 16 minutes into the second half for ZESCO, who lacked injured leading scorer Alfred Luputa, one of just four footballers to score a hat-trick in a Pan-African club competition this year.
The giant-killing run of Kenyan outfit Sokapaka appears over after a 3-0 defeat in Tunisia by Club Africain, who were ahead within four minutes through Khaled Melliti and he scored again before Hamza Messadi converted a penalty.
Algerian challengers had mixed fortunes with Entente Setif taking a narrow 1-0 home lead over Kaduna United of Nigeria while a JS Kabylie side depleted by injuries and suspensions left Senegal happy after holding Diaraf 1-1 in Dakar.
Abderrahmane Hachoud turned a defender twice inside the penalty area before scoring a 77th-minute winner for Setif and Babacar Ndiour levelled for Diaraf six minutes after Nabil Yalaoui had given Kabylie an early second half lead.
Return matches are scheduled for the weekend of 10-12 June when Simba of Tanzania host Daring Club Motema Pembe of the Democratic Republic of Congo in a postponed fixture. The Libyan conflict has once again prevented Al-Ittihad playing in Tripoli and the tie with Sunshine Stars of Nigeria has been reduced to a single match at the ground of their opponents.