The third-seeded Rams (22-8) advanced to the semifinals Saturday at Barclays Center against No. 2 Dayton. The top defensive team in the conference, Rhode Island held GW to 31.1 percent shooting.
Jarvis Garrett had 12 points, six rebounds and six assists for the Rams, who won only 14 games last season.
Patricio Garino led sixth-seeded George Washington (21-12) with 17 points and 10 rebounds.
Rhode Island took a 47-43 lead with an 8-0 run, capped by Hassan Martin's dunk with 9:45 left in the second half.
Matthews swished a 3 to put Rhode Island up 59-50 with 5:02 left.