The Eagles (3-7) scored 22 straight points and held Stony Brook scoreless for the final 11:49 of the first half en route to the win.
Bryan Dougher led the Seawolves (3-5) with 21 points. Stony Brook missed its last 13 shots of the opening half and shot 15.2 percent (5 of 33).
It was the lowest point total in any half ever at Conte Forum, which opened in 1988.
Boston College trailed by five points a little over 8 minutes into the game before going on the spree that turned an 11-6 deficit into a 28-11 halftime lead.
BC, which had 10 turnovers in the opening 13 minutes, overcame a sluggish start to shoot 50 percent (11 of 22) from the floor in the first half.
Eagles coach Steve Donahue was upset with the play of starting point guard Daniels and pulled him from the game when Stony Brook led by five.
When he returned to the floor 41 seconds later, Daniels got BC's offense going with a driving basket and the Eagles started nailing shots from the outside. Lonnie Jackson and Heckmann each hit a pair of 3s during a stretch of 2:12 in the game-breaking spree. Daniels also hit a pull-up jumper during the run and Dennis Clifford had a pair of baskets.
The Seawolves -- behind Dougher's steady scoring after intermission -- closed the gap to nine points three times in first 10 1/2 minutes of the second half, but the Eagles were able to keep them from threatening any further with timely baskets.
Stony Brook closed it to 47-39 on Dougher's 3 with 8:29 left, but Anderson had a dunk and then hit two free throws on the next possession to make it 51-39.
Stony Brook, picked second in the America East Conference's preseason poll, hosts Rutgers, from the Big East, on Saturday. The Seawolves lost a pair of games against Big Ten teams -- at Indiana and Northwestern -- earlier this season.
The Eagles, picked last in the Atlantic Coast Conference, host Bryant next Sunday. They don't open conference play until they travel to North Carolina on Jan. 7.
Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.
NBA fans will be looking forward to their newest players making plays like this next season.