Chavaughn made 10 of 19 shots from the field and Price hit 9 of 17 for the Red Foxes, who had their best shooting outing of the season, hitting 54.8 percent (34 of 62) of shots from the field.
After 11 lead changes over the first 5 minutes, Marist (4-6) took the lead for good, 13-12, behind a dunk from Manny Thomas. A 3-pointer by Price put Marist ahead 40-31 with 2:37 left to play.
Dorvell Carter scored Marist's final eight points of the half to send the Red Foxes into the break with a 48-31 lead.
Justin Edwards' 23 points paced Maine (3-8), which had four starters in double-figures but got just five points off the bench. Marist's bench contributed 21 points.