Forward-center Monroe came off the bench to top the Bengals (3-9, 0-0 Big Sky) with 16 points. He hit eight of 11 field-goal attempts and pulled down 12 rebounds. Stucki, a guard, had 10 assists and 10 points, plus seven rebounds.
The teams traded leads in the first half, with ISU leading 36-34 at halftime.
ISU led by as many as 12 points in the second half, but the Crusaders cut the lead to two points at 66-64 with 1:36 remaining in the game.
The Bengals pulled out the win with a layup by Monroe, a pair of foul shots by Stucki and a free throw by Morgan.
Northwest Nazarene (8-1, 0-0 Great Northwest Athletic Conference) was led by center Scott Helpenstell, who scored 16 points and grabbed nine rebounds. Kendall Gielow and Joel Ryman each added 13 points for the Crusaders, and Louie Beech had 10.
ISU outrebounded the Crusaders 37-27.