Badau Diagne tallied 12 for Coastal Carolina (13-12, 8-6 Big South Conference). Raffa, who made 8 of 16 shots and four 3-pointers, gave the Chanticleers a 63-62 lead with 35 seconds left on his lone free throws of the night.
UNC Asheville (15-13, 9-5) regained the lead on D.J. Cunningham's dunk with 21 seconds showing, but Coastal Carolina called a timeout to set up Greenwood's game-winner.
With a chance to win it, the Bulldogs' Trent Meyer missed a 3-pointer at the buzzer.
Both teams shot 46 percent, 25 of 54 for Coastal Carolina and 23 of 50 for UNC Asheville, but the Chanticleers scored 34 points off 22 Bulldogs turnovers.
Jeremy Atkinson had 18 points for UNC Asheville, which was outscored 40-26 in the paint.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.