Tuch scored glove side from the slot off a drop pass from Dylan Cozens.
"Four points, he was incredible," Sabres coach Don Granato said. "Obviously, it was his night to rise, dictate, influence, take over. He's had a solid NHL career so far, but the potential that he has, it's enormous. He hasn't even scratched the surface, and a night like tonight is what we've been talking about."
Cozens had a goal and an assist, and Ukko-Pekka Luukkonen made 37 saves for the Sabres (18-14-2), who have won six in a row and are 11-3-2 since losing eight straight in regulation from Nov. 4-19.
"We knew going into the third that they obviously hadn't lost in regulation (at home), and we wanted to be that first team to do that," Cozens said. "Obviously, they battle back, and then we take the two penalties to make it 5-on-3. The kill just did a great job, and 'UPL' did an outstanding job with some huge saves. We just found a way, and that shows the kind of team we are this year. We don't want to back down from anyone, and we know when adversity (happens) we can overcome it and win hockey games."
Brad Marchand and David Pastrnak each had a goal and an assist for the Bruins (28-4-4), who extended their season-opening home point streak to 21 games (18-0-3). Jeremy Swayman made 21 saves.
Boston will next play the Pittsburgh Penguins in the 2023 Discover NHL Winter Classic at Fenway Park on Monday (2 p.m. ET; TNT, SN, TVAS).
"Disappointing finish," Marchand said. "We had that game, we had our hands all around it and kind of squandered it. That's on us. We should have been much better in that situation, but we're not going to dwell on it. We got a point and we've got a great opportunity ahead of us. We're going to have a lot of fun (in the Winter Classic). It's an exciting time."