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.
Gonzaga has signed California transfer Jordan Mathews to a financial aid agreement for the 2016-17 season.
Coach Gilmore on CWS win: 'It's indescribable' Coastal Carolina head coach Gary Gilmore reflects on his 21 years as head coach and is proud of how far the program has come.
Two late June events provided a great start on the 2020 class and a look at some new 2019 talent.