Western Michigan (23-10), the Mid-American Conference champion, had won 14 of 16 games and was in the NCAA tournament for the first time in a decade.
The Orange forced 11 turnovers in the opening half and scored 13 points off them in running out to a double-digit lead before the midpoint of the period.
Cooney led the Orange with 18 points, hitting 4 of 8 from beyond the arc, and Ennis had 16 points and six assists with one turnover and two steals.
The Orange used an 18-4 spurt over 10 minutes to take control and led 40-21 at halftime.
Shayne Whittington and Tucker Haymond led Western Michigan with 11 points apiece.