Brewer hit two 3-pointers to give the Eagles (21-8, 11-3 Patriot League) an 85-81 lead in the second overtime after the Leopards (11-18, 6-8) scored first on a pair of free throws by Jared Mintz.
Brewer, who made 5 of 9 3-pointers overall, had eight points in the second overtime, and his three-point play tied the game at 67 at the end of regulation.
Tony Johnson scored 29 points for Lafayette, including seven in the first overtime, and Mintz had 26 points and nine rebounds.
The loss was costly for the Leopards, who could have earned the No. 3 seed in the conference tournament but instead dropped to No. 6 and will play at Holy Cross on Wednesday. American University, the No. 2 seed, will host Colgate.