Using solid shooting and a stingy defense, the Catamounts (25-9) took an early lead and never trailed.
Boston (19-13), which lost both regular-season games, shot 38 percent and struggled with its offensive flow. Leading scorer John Holland, who averaged 19.3 points, was held to nine points in the title game. It paired the top two teams in the America East's preseason poll.
The hosts, winners of 10 of their last 11, hit their first four shots of the game and took a 17-14 lead on the strength of deep 3-pointers by Joey Accaoui and Garvey Young.
Boston's marksman was Corey Lowe, who hit a pair of NBA-long three-pointers en route to 12 first-half points. But the Terriers shot 35 percent from the floor in the first half — to 64 percent for Vermont — and Holland hardly touched the ball.
Meanwhile, everyone on the Catamounts' side was contributing.
Guard Nick Vier hit a three-pointer off a low-post kick out pass from Blakely, who added an up-and-under lefthander to extend the lead to 24-14. That was Vermont's biggest lead until Blakely hit an off-balance turnaround at the buzzer for a 42-31 edge at the break.
Boston (19-13) mounted a second-half rally, getting a pair of baskets from Jake O'Brien and a 3-pointer by Corey Lowe to narrow it to 54-53. That was as close as they got.
Blakely, a high-flying 6-foot-5 forward, put the icing on the cake with a thunderous one-handed slam off a 3-on-2 break with 1:34 left.
Vier added 15 points and Maurice Joseph had 13 to give the Catamounts their first NCAA bid since 2005, when they stunned Syracuse in a first-round overtime thriller.
Lowe had 24 points, O'Brien 17 and Carlos Strong 11 for Boston.
The sellout crowd of 3,266 in Patrick Gym rushed the floor after the final buzzer, mobbing Blakely and his teammates before the cut down the nets.
"Your Vermont Catamounts are dancing to the NCAAs!" yelled the public address announcer.