Munford scored 14 points in the second half, including 11 during a 16-3 run when the Rams (5-8) extended a five-point lead to 43-25 with 4:20 remaining.
Both teams shot poorly in the first half, which ended with the Rams ahead 21-14 despite shooting 25.8 percent (8 of 31). The Bears (4-8) shot 25 percent (5 of 20). Rhode Island's Andre Malone scored 10 of his 12 points in the half.
Powell's 3-pointer put Rhode Island ahead to stay, 12-10, with 10:27 left until halftime.
Rhode Island has won 10 of its last 11 meetings with Brown and leads the series 101-53.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.