Connor Dewar and Mantha scored 33 seconds apart early in the third period for the Penguins.
Dewar spun off Aspirot in the left circle for a backhand, cutting it to 3-2 at 6:02; Mantha scored on with a backhand on a semi-breakaway to tie it 3-3 at 6:35.
Zacha put the Bruins back in front 4-3 at 8:34 with a wrist shot off a pass from Arvidsson behind the net. He scored three goals in a 10-2 win against the New York Rangers on Jan. 10 for his previous hat trick.
“I think it was a good feeling in the moment,” Zacha said. “I think after a loss, you don’t really think about it anymore. We were leading most of the game, so it was a good feeling. I was able to score the third goal, but right after the game, it kind of goes away if you don’t win.”
Mantha tied it 4-4 at 11:18 by knocking down a point shot from Parker Wotherspoon and chipping it in from the crease for his 23rd goal this season.
Zacha put Boston ahead 1-0 on a power play at 9:27 of the first period, dropping to one knee in the right face-off circle for a one-timer.
He made it 2-0 at 8:47 of the second period, stickhandling around Pittsburgh forward Ben Kindel before lifting a backhand over Silovs.