Kierre Greenwood had 10 points, and Badou Diagne pulled down 10 rebounds for the Chanticleers (12-11, 7-5). Greenwood's two assists moved him past Dwight Lighty into second place on the career list with 461.
Coastal outrebounded Presbyterian 45-27, and the Chanticleers' 22 offensive rebounds gave them a 19-4 advantage on second-chance points.
The Chanticleers led 48-40 on Raffa's 3-pointer and El Hadji Ndieguene's free throw with 8:15 remaining.
McTavish hit two foul shots to close to 52-48 at 2:31, and Mutakabbir's 3-pointer got them to 57-53 at 0:44, but Raffa's two free throws sealed it.
The Big East has joined the ACC, Atlantic 10 and Colonial Athletic Association in forming a men's basketball officiating alliance.
Nebraska guard Andrew White, who averaged 16.6 points and 5.9 rebounds per game last season, will transfer from the program and is eligible immediately. What else is on Dickie V's mind this week?
The Cavaliers bring in a top-10 class of four incoming freshmen, so the Class of 2017 will be a small one. Coach Tony Bennett is aiming high.