Ibrahim Mustapha scored the only goal of the game after seven minutes as Enyimba moved to six points and leapfrogged the Ivorians, who have two points fewer.
In the other game in the pool, Djobila moved into second place with a comfortable 2-0 home win over CARA Brazzaville.
Goals either side of halftime from Mamadou Cisse and Mahamadou Coulibaly sealed the three points for the home side.
Enyimba head the group, followed by Djobila and Williamsville AC on four points, with CARA on three.
Raja Casablanca moved to the top of Group A after an excellent 1-0 away win at ASEC Mimosas.
It took a penalty 15 minutes from time via Mahmoud Benhalib to give the visitors the three points, while ASEC finished the match with 10 men after a red card for goalkeeper Abdoul Cisse.
Cisse received his marching orders for connecting with an opponent as he tried to punch the ball clear, and having used all of their substitutes already, striker Issa Sanogo had to go in goal.
Benhalib converted the spot-kick and Raja comfortably held on for the remainder of the game.
Ghana's Aduana Stars claimed a vital 2-1 win over AS Vita Club in the other match in the pool, with all the goals scored in the opening 26 minutes.
Stars were 2-0 up early through strikers Bright Adjei and Yahaya Mohammed, but when Glody Ngonda pulled a goal back for the DR Congo side it was game-on.
Vita Club were not able to force an equaliser though and Raja top the pool with five points, followed by Stars and Vita Club with four each, and ASEC with three.
Moroccan side Berkane remain top of Group B despite being held at home by Egyptian club Al-Masry following a 0-0 stalemate.
Al-Hilal misses the opportunity for three precious points when they let a two-goal lead slip to draw 2-2 at home to Mozambique outfit UD Songo.
The Sudanese side seemed destined for the win when Mohamed Bashir and Thomas Ulimwengu gave them a first half lead.
But Malawian Frank Banda pulled a goal back for the Mozambicans, who found an equaliser three minutes from time via former Orlando Pirates forward Hélder Pelembe. Berkane lead the pool with seven points, followed by Al-Masry (five), Al-Hilal (two) and Songo (one).
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