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.
White House officials said Tuesday that the Villanova men's basketball team will visit with President Barack Obama next week.
Kendrick Nunn, who pleaded guilty to misdemeanor domestic battery last week, has been dismissed from the Illinois basketball team.
Delaware has hired Notre Dame assistant Martin Ingelsby as its next men's basketball head coach, sources told ESPN's Jeff Borzello.