Reinhart tied it 1-1 on the power play on a one-timer from the left circle at 15:40.
Dahlin's shot from the high slot through a crowd in front of Rask gave the Sabres a 2-1 lead at 6:54 of the second period. Casey Mittelstadt scored from the bottom of the right circle to extend it to 3-1 at 14:17.
Arttu Ruotsalainen made it 4-1 from the high slot at 1:14 of the third period, and Rask was pulled.
Reinhart beat Halak to a loose puck on the power play to push it to 5-1 at 4:30.
"Any goal support you can get for your goaltender, it helps," Granato said. "We fell behind 1-0, you know the statistics in this league when you fall behind 1-0. They're not good. So for our guys to stay on it, continue to just stay with the game plan and stay focused and work and get rewarded for it obviously made things much easier for [Luukkonen], and he did his job all the way through, I felt."
Nick Ritchie poked in a rebound from to make it 5-2 at 12:06, and Kevan Miller cut into the slot to narrow it to 5-3 at 15:25.
With an extra attacker, Hall brought the Bruins to within 5-4 at 17:12 when his shot from the right circle went in off the stick of Sabres defenseman Rasmus Ristolainen in front.
"I think we just got away from our game plan," Kampfer said. "It's tough to win hockey games when you show up for the last eight, nine minutes of the game. It's on us in the room. It's the National Hockey League, every team's good, everybody can beat everybody. We've got to show up and play games like that. That's on us in the room to make sure that when 7 o'clock rolls around, we're ready for 60 minutes."
Reinhart scored into an empty net with 42 seconds remaining for the 6-4 final.
Bruins center Patrice Bergeron was a late scratch with a lower-body injury.
"Obviously he's our No. 1 center, so we miss him in a lot of situations but we're a pretty good team, we've got depth," Cassidy said of the Boston captain. "He's a big part of every facet of our game, but there's other guys here capable. I don't think he had any effect on guys not being hard enough on pucks or playing a more determined game. That's on the individual and on me to get it out of them. We miss him, but certainly not the cause for defeat tonight."
NOTES: Luukkonen was selected by the Sabres in the second round (No. 54) of the 2017 NHL Draft. … Bruins forward David Pastrnak had his point streak end at five games. … Reinhart had his fifth multigoal game of the season, second in the NHL behind Auston Matthews of the Toronto Maple Leafs, who has eight.