The Catamounts (7-9, 1-1), coming off a 65-59 league loss at Stony Brook, won their home opener for the 11th time in their last 12 tries.
Brian Voelkel matched his career high with 16 rebounds as Vermont outrebounded the Terriers 42-31.
BU, the America East preseason favorite, led by five early, but the Catamounts used a 9-0 run to pull ahead for good.
After the Terriers (4-11, 0-1) got to 35-32, Brendan Bald's 3 sparked a 6-0 run and BU could get no closer than five after that.
Luke Apfeld added 13 points for Vermont, which shot 26 of 57 from the field and 25 of 31 from the line.
Darryl Partin's 19 points paced BU, which has lost 10 of its last 13 to Vermont.