Tage Thompson scored his team-leading 27th goal and Ukko-Pekka Luukkonen stopped 37 shots for the Sabres, who won for just the second time in their last 11 games against the Bruins.
''Everybody knows how good they've been at home,'' Luukkonen said in a joyful and loud Sabres' locker room. ''I feel like guys are really confident now and it shows.''
Trailing 3-2 and skating with an extra attacker after pulling its goalie, Buffalo tied it when Dylan Cozens slipped a wrister past Jeremy Swayman with 1:37 to play.
''We came in here and I thought a lot of guys really showed up and worked really hard,'' Tuch said. ''We're finding examples where we allow skill to take over. We got a little lucky, but we'll take it.''
Boston's Brad Marchand had scored the go-ahead goal on a clean breakaway after setting up Patrice Bergeron's tying score just over five minutes into the third period.
''There's always something to learn - win or loss,'' Marchand said. ''We realize that any team can win any game. When we're up late like that we have to have the killer instinct. We didn't tonight. Definitely something we have to be better at down the road and playoff time.''
David Pastrnak added his 25th goal and Swayman made 21 saves for the Bruins, who remained unbeaten in regulation at home at 18-0-3.
Tuch slipped a shot past Swayman from the slot for the game-winner.
''It was relieving,'' Tuch said. ''I was a little tired. A couple of long shifts.''
Boston failed to add to its lead with a 5-on-3 power play late in the game.
''In that situation, with time on the clock and the amount of time we have on the 5-on-3, I think we have to extend the lead there,'' Bergeron said.
Marchand had collected Pastrnak's pass, skated up the middle and slipped a wrister between Luukkonen's pads.
Bergeron's tying score came when he one-timed Marchand's pass from the edge of the right circle.
Tuch skated in on a breakaway and slipped a wrister inside the left post to put the Sabres ahead 2-1 early in the second period.
Boston had taken a 1-0 edge at 13:09 of the first when Pastrnak one-timed David Krejci's cross-ice pass, but Thompson collected the puck in front of the net and shifted around Swayman before tucking it in at 16:13 of the period.
Bruins coach Jim Montgomery didn't hesitate when asked if he was worried about his team looking ahead to the Winter Classic matchup against the Pittsburgh Penguins at Fenway Park on Monday.
''Usually I'd be very concerned about that, but not with this group,'' he said. ''They are very, very professional. We just talked about the importance of our keys to having success against the Sabres, who are a very, very dangerous offensive team.''
SPLENDID EARLY STOPS
Swayman made a left-arm save on Peyton Krebs' breakaway early in the first period after Luukkonen went sprawling to make a left-pad stop on Nick Foligno's shot.
NOTES: Bruins forward Tomas Nosek missed his second straight game with an undisclosed injury, but Montgomery said beforehand that ''he's doing better. Do expect him to play in the Classic.'' . Thompson has a team-leading 51 points. . Boston won the first meeting between the teams, 3-1, in Buffalo on Nov. 12.
Sabres: At the Ottawa Senators on Sunday night.
Bruins: Winter Classic on Monday at Fenway against the Penguins.
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