Reggie Jackson added 11 points for Boston College (4-2), which won 2 of 3 during the four-day tournament. The Eagles beat Texas A&M 67-65 and lost 65-55 to Wisconsin.
Jackson and Danny Rubin each hit 3's as Boston College scored the first eight point of the second half to go up 43-31 with 17 minutes to play. Rubin added another 3-pointer to extend the Eagles' advantage to 49-33 at the 5 minute mark.
Trapani had a 3 during an 8-0 run that put Boston College ahead 61-38 midway through the second half.
Boston College led 35-31 at halftime despite the Eagles' top two scorers, Jackson and Trapani, combing for just four points.
California (3-2) got 12 points from Jorge Gutierrez. The Golden Bears lost their final two games at the classic after beating No. 21 Temple 57-50 in Thursday's opening round.
California got nine first-half points from Gutierrez, which was more than the entire Golden Bears team scored in the opening 20 minutes of Friday's 57-44 loss to Notre Dame. The Fighting Irish had a 21-5 halftime advantage en route to the second-round victory.
Boston College shot 49 percent (24 of 49) and made 10 of 16 free throws.
California made just 35.4 percent (17 of 48) of its shots and wound up 5 of 10 from the foul line.