The win is the Chanticleers' (9-9, 4-3) first against Campbell since Dec. 20, 2003.
Raffa scored 20 points and Greenwood 18 for Coastal Carolina, which shot 49 percent (24 of 49) and made 22 of 31 free throws.
The Camels entered having won seven of their past eight games with a 48.6 shooting percentage. Saturday, Campbell hit just 37.5 percent (21 of 56), and Trey Freeman, who was averaging 16.6 points per game during the run, had just two points on 1-of-11 shooting.
Coastal Carolina snapped a 22-22 tie with a seven-point run to close out the first half, then scored the first six of the second half for a 35-22 lead.
Shooting guard Jaylen Nowell, ranked No. 45 in the ESPN 100, chose the Washington Huskies on Wednesday over California. As a junior he led Garfield Heights to a state championship and was named MVP of the tournament.
Donnie Tyndall has filed an appeal to reverse the 10-year show cause penalty he received from the NCAA in April for violations that occurred while he was coaching Southern Mississippi.
Top-50 prospect Jaylen Nowell committed to Washington on Wednesday. Nowell, a shooting guard, is No. 45 on the ESPN 100.