Cooks followed his career-best 22-points in the Eagles 102-95 opening victory against Hampton, with 7-of-12 shooting from the floor. Keon Johnson and Bjorn Broman scored 15 points with four 3-pointers apiece for Winthrop (2-0).
Andretti Loyd scored 19 points with five 3-pointers, and J'Quayveon Williams added 13 to lead Truett McConnell.
The Eagles led 49-45 early in the second half. Cooks scored straight six points to spark a 24-7 run and the Eagles led 73-52 midway through the second half.
It was the first meeting between the schools.