With the game tied at 62, back-to-back 3-pointers by Jared Nickens and Sulaimon gave the Terrapins (4-0) a six-point cushion with 3:45 left.
The Redbirds (2-3) tried to rally, but a strong Maryland defensive showing forced 17 ISU turnovers on the night.
The Terps are now outscoring opponents 59-30 in the final five minutes of games this season, an average of plus-7.25 per game.
Damonte Dodd registered a career-high in points with 13, including 12 in the second half. Trimble added seven assists as five Terrapins recorded double-digit scoring, including Jake Layman (12) and Robert Carter (11).
"This was the best we've played - especially defensively," head coach Mark Turgeon said. "Damonte was great tonight. I am proud of my team because we played an Illinois State team that was really great tonight."
Maryland will face Rhode Island for the Riviera Division title on Wednesday at 8:30 p.m. on the CBS Sports Network. Illinois State plays TCU in the consolation game.