Josh Southern chipped in with 13 points and nine rebounds for the Eagles (12-2), who open Atlantic Coast Conference play at No. 1 North Carolina on Sunday.
A major snowstorm kept the crowd small, with no more than 700 fans showing up for the game.
BC led just 47-44 early in the second half before it started pounding the ball inside and took control of the game. BC scored nine of its next 20 points from the free throw line to take a 67-56 lead it wouldn't lose.
The loss was Sacred Heart's fourth in its last five games.