Lamar Patterson added 16 points and Cameron Wright 14 for the Panthers (21-7, 9-6 Atlantic Coast Conference). Olivier Hanlan led Boston College (7-21, 3-12) with 25 points and Patrick Heckmann had 15. The Eagles have lost seven of their last eight games.
Hanlan reached the 1,000-point mark late in the first half, becoming just the third player in school history to accomplish the feat as a sophomore.
Pittsburgh's 14-point lead was sliced to 49-45 on Hanlan's two free throws with 8:50 to play, but less than a minute later Heckmann was called for a flagrant 1 foul on Zanna, who hit both from the free-throw line.
After Joe Rahon missed a 3 from the top for BC, Zanna hit two more from the line, pushing Pitt's lead to 53-45 with just under 7 minutes left.
The Eagles never narrowed the deficit below a two-possession game the rest of the way.
When the Eagles did slice it to 59-53, Zanna had a three-point play and later added a putback to help the Panthers hang on.
The Panthers had pushed their nine-point halftime edge to 40-26 on Patterson's 3-pointer in the opening minutes of the second half. But BC scored 11 of the next 13 points, closing it to five on Garland Owens' free throw with just over 15 1/2 minutes to play.
Pittsburgh led 35-26 at halftime.
The Panthers shot 53.8 percent in the opening half (14 of 26) and dominated on the glass, collecting as many offensive rebounds (seven) as BC had total.
The only thing Pitt didn't do well in the first half was handling the basketball as it committed eight turnovers, more than half, though, came in the early minutes.
BC's 2/3 zone gave Pitt trouble for about 2 1/2 minutes. After coach Jamie Dixon called a quick timeout, the Panthers took control with a 28-8 run over the next 12 minutes that was filled with wide-open shots and transition baskets. Patterson scored eight points during the spree.
Pittsburgh's losing streak started with a buzzer-beating loss at home against Syracuse on Feb 12.
The Panthers have won 20 games for 13 straight seasons. It was the first ACC matchup for the schools, who last met as members of the old Big East in 2005.