The at the Adokiye Amiesimaka Stadium in Port Harcourt
Enyimba fell behind in the 31st minute through a goal by N'da Jean-Willy Kouakou.
The People's Elephants tried to equalise but could not as they went into the break a goal down.
After a back and forth of chances created by both sides, Enyimba fell further behind through a goal by Guy Cedric Yameogo in the 71st minute.
Enyimba could not find their way back or get a consolation as they lost 0-2 away from home in their first game since the resignation of .
The result means that Willamsville of Ivory Coast top the group with seven points, Enyimba are tied on six points with Cara Brazzaville of Congo, while Malian side Djoliba have just four points.
Enyimba will have to finish in the top two in their group to progress to the next round of the competition with just two group games left to play
Enyimba's group stage fixtures
Away vs Djoliba Sunday, August 17
At home vs Cara Brazzaville, Wednesday, August 29.