The Patriots (5-2) led by as many as 16 and 35-22 at halftime.
The Rams (1-6) pulled ahead 38-37 with 12:44 remaining, with Xavier Munford scoring eight points in the 16-2 run, but their lead lasted just 21 seconds.
The game was tied three more times before George Mason built a five-point lead, capped by a Wright layup with 3:09 left.
Rhode Island got within two, at 54-52 with 2:10 left, but missed its final three field goal attempts, including Nikola Malesevic's 3-point try with 3 seconds remaining.
George Mason had a 50-31 rebounding advantage, and its 19 offensive boards resulted in 22 second-chance points.
Munford's 24 points led the Rams, who made only 13 of 26 free throw attempts.
Myron Medcalf and Amin Elhassan discusses the Nets' selection of Caris LeVert with the 20th overall pick.
Myron Medcalf and Amin Elhassan discuss the Nuggets' selection of Malik Beasley with the 19th overall pick.
Myron Medcalf and Amin Elhassan discuss the Pistons' selection of Henry Ellenson with the 18th overall pick and how he'll pair up with Andre Drummond.