Kurt Steidl added 13 points and seven rebounds for Vermont (13-9, 5-2 America East). O'Day and Steidl scored 20 of Vermont's 31 first-half points as the Catamounts led by seven at halftime.
The Catamounts shot 44 percent from the field while New Hampshire (11-9, 4-3) shot 24 percent.
Steidl's 3 at the 13:13 mark of the second half pushed Vermont's lead to 46-29.
Vermont is 30-6 against the Wildcats since the 2001-02 season - including 11 of the last 15 meetings.