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.
Former Michigan point guard Spike Albrecht will play for Purdue as a graduate transfer next season.
Only six major-conference teams have failed to win an NCAA tournament game since the turn of the century. When will each program snap the streak?
Bruce Weber's Kansas State team earned a share of the Big 12 title three years ago, but a lot has changed since then and the pressure is on.