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.