Brown jumped out to a 17-3 lead and never trailed in the game. The Bears used an 8-2 run late in the first half to open up a double-digit lead and took a 42-33 lead into the break.
An 8-0 run by Brown, capped by a McGonagill 3-pointer with just fewer than 11 minutes left, pushed the Brown (12-8, 4-2 Ivy League) lead to 58-45.
John Golden hit 1-of-2 free throws with 6:57 remaining to pull Dartmouth within nine, but McGonagill hit another 3 just 25 seconds later and the Big Green never got closer than 10 points the rest of the way.
Golden paced Dartmouth (9-11, 2-4), which shot just 33.9 percent, with 17 points.
Rafael Maia scored 13 points and grabbed 10 rebounds for Brown.