The victory ended Providence's (14-11, 6-7 Big East) nine-game losing streak to the Irish (20-6, 8-5), who won an epic five-overtime contest against Louisville last weekend and then beat DePaul in OT on Wednesday.
Batts was 10-for-13 from the field and Cotton sank a trio of 3-pointers.
Providence shot 43.9 percent from the field to 40 percent for Notre Dame. The Irish were 1-of-14 from 3-point range and committed 11 turnovers.
Jack Cooley led Notre Dame with 12 points and 10 rebounds. Tom Knight and Garrick Sherman both scored 11 points.
Swim Week Miami Beach 2014 [PHOTOS]