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.
Purdue coach Matt Painter says players haven't used the fifth-year graduate transfer rule for its true intent.
The dust has settled after players made their NBA draft decisions. Which college teams won? Which lost? Well, Villanova is pretty happy. USC, meanwhile, might not be as thrilled.
The 2017 recruiting class is short on point guards, with Trevon Duval leading only eight prospects from the ESPN 60 who are still available.