Abdelkader Ghorab netted the winning goal for the home team in the 64th minute.
It was Enyimba's second defeat in the group following their 2-0 loss on Matchday One to Morocco's Hassania Agadir.
In the other Group D game, San- Pedro of Cote dl voire were held to a 1-1 draw at home by Hassania Agadir.
Hassania Agadir top the table with seven points, while Paradou are second with four points.
Enyimba occupy third position with three points, while San-Pedro are fourth with two points.
Meanwhile, Rangers of Enugu held their hosts Nouadibou of Mauritania to a 0-0 draw in a Group A encounter at Stade Cheikha Ould Bodiya.
Rangers had lost their opening two games in the group to Al Masry and Pyramids of Egypt.
In the other Group A encounter, Pyramids of Egypt defeated Al Masry 2-1 to go to the top of the group with nine points, while Al Masry are second with six points.
Rangers and Nouadhibou are third and fourth respectively with a point each.