Larsen and McDonald each made five shots from the field while Lasan Kromah, who had led George Washington (3-3) in scoring the past two games, finished with 10 points on 4-of-6 shooting.
The game went back-and-forth, as neither team led by more than four. Charles Cooke broke the games' seventh tie with a free throw to put James Madison (1-5) up 48-47 with 3:12 left.
But the Dukes would not see the lead again, as Larsen hit a layup to help George Washington retake the lead, 52-48, and Patricio Garino hit a 3-pointer to put the Colonials ahead for good.
James Madison scored just one basket over the final two minutes before Andre Nation sank a desperation heave at the buzzer.