Trimble, who was named tournament MVP, also went 3 for 3 at the line and grabbed six rebounds.Rasheed Sulaimon also scored 17 points on 6-for-7 shooting, and Robert Carter had 15.
"We got stronger as the tournament went on. We get better very game, and we looked better tonight because we made shots," Maryland coach Mark Turgeon said. "We were dialed in defensively and seemed to have a lot of energy. The only frustrating part was foul trouble, and we gave up a ton of layups in the second half."
After playing three straight games that required a second-half comeback to get the victory, Maryland (5-0) was in control throughout against the Rams (3-2). Trimble hit a long jump shot at the first-half buzzer to make it 44-28, and Rhode Island struggled to keep up the rest of the night.
With a high-profile matchup with North Carolina looming on Tuesday, the Terrapins looked very comfortable, shooting 60 percent from the field and playing stout defense on Rhode Island. The Rams shot just 34 percent from the field, including a 2-for-15 performance from 3-point range.
"We beat a really good team handily, one that is well-coached. What we do care about is, we're getting better," Turgeon said. "We had to accept that just because you are ranked high doesn't mean you will win every game easily. We're going through a process we haven't gone through before. We're getting deeper as a team, dialing in — a lot of things are headed in the right direction."
Both benches were assessed a technical foul late in the second half, and there was some tension between the teams before the awards ceremony after the game. But there were no other incidents.
Kuran Iverson scored 19 points for the Rams, and Earl Watson had a career-high 17 points.
Maryland freshman center Diamond Stone was in foul trouble for the second consecutive game, but he finished with 10 points, five rebounds and three blocked shots.
Coming into the night, the Terrapins were shooting barely 30 percent as a team from 3-point range, but were a solid 10 of 17 from long range against the Rams.