Zacha had three assists, and Jeremy Swayman made 21 saves for the Bruins (59-12-5), who have won nine of 10.
Boston, which has already won the Presidents' Trophy, has 123 points this season, the most in its history.
"It's a great accomplishment, but it's hard when you're right in the moment to embrace it, I guess maybe enjoy it," Bruins coach Jim Montgomery said. "I think after the season is over, we'll be able to sit back. It's historical what we're doing. It's a pleasure to coach these guys."
Bryan Rust had two goals and an assist, and Jake Guentzel extended his goal streak to four games for the Penguins (37-29-10), who have lost seven of 10 (3-7-0). Tristan Jarry made 31 saves.
Pittsburgh fell one point behind the Florida Panthers for the second wild card into the Stanley Cup Playoffs from the Eastern Conference. Florida defeated the Columbus Blue Jackets 7-0 later on Saturday.
"We've got to find a way to get over it," Penguins coach Mike Sullivan said. "It was a tough way to lose tonight. It was a tough way to lose, and that stings when the games have so much meaning, like they do at this time of year. But we've got to find a way to get over it. That falls on all of us, myself included."