Matt Glass had 19, Clancy Rugg 15, Luke Apfeld 14 and Brendan Bald 11 for Vermont (19-10) in the Bracket Busters matchup.
McGlynn connected on six 3-pointers while Rugg grabbed 12 boards to lead Vermont to a 42-22 rebounding advantage.
Vermont jumped out to an early 13-3 lead and pushed that lead to 16, 23-7, behind a 3-pointer from Bald.
Niagara (12-17) cut the deficit to 31-22 but Vermont outscored the Eagles 21-7 over the final 6:34 of the first half to take a 52-29 lead into halftime.
Vermont led by at least 18 points throughout the entire second half.
The Catamounts converted 20 of 22 free throws.
Antoine Mason led Niagara with 20 points and Malcolm Lemmons had 17.