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 that cut it to 3-2 at 6:02. Mantha scored with his own backhand on a partial 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, who was behind the net. His only previous NHL hat trick came in a 10-2 win against the New York Rangers on Jan. 10.
“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.
“They had us for two periods there,” Mantha said. “We came in here between the second and the third, we just knew it was going to feel good. We said it in here. … It actually feels really good.”
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.