The 21-year-old Nigeria striker opened the scoring in the 12th minute to give Les Hurlus the lead.
In the 41st minute, Selim Amallah increased the lead before Babacar Dione sealed the win in the 55th minute.
Awoniyi featured for 76 minutes before he was substituted for Manuel Benson.
Despite the emphatic win, Royal Excel Mouscron remain in the bottom of Group B with four points from seven games as Kortrijk continue to lead the group with 18 points.
The Super Eagles are in Group B along with Burundi, Guinea and Madagascar.