Cooley, a senior, blocked three shots while going 5-of-7 from the field for the Fighting Irish (1-0), who are coming off a second-round loss in last season's NCAA Tournament.
Jerian Grant helped out with 11 points for Notre Dame.
The Aces (0-1) got 15 points from Colt Ryan in their 2012-13 debut. Ryan Sawvell chipped in with 10 points and 11 rebounds for Evansville.
2014: The Year in Music [PHOTOS]