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.