McLaughlin hit a jumper to stretch Bryant's lead to 61-57 with 45 seconds remaining and - after Dartmouth's Evan Boudreaux cut it to 61-60 with a three-point play - sank a free throw with 16 seconds left for the final margin.
Malik Gill's 3-pointer for Dartmouth missed with five seconds left and, after a scrum underneath, freshman Nisre Zouzoua came away with the ball for Bryant (3-10). Zouzoua scored 13 points with three rebounds.
Boudreaux and Miles Wright each scored 16 points for Dartmouth (4-7) and Boudreaux also had 13 rebounds.
Bryant shot 10-for 18 from 3-point range, McLaughlin going 4 for 4 and Zouzoua 3 for 5.
The win was Bryant's first in four games this season against the Ivy League.