Dahlin scored Buffalo's lone goal of the game with 1:47 remaining in the first period. Carter Hutton stopped 39 of 40 shots filling in for Linus Ullmark, who had been scheduled to start before aggravating a minor injury during the team's morning skate.
Nikita Kucherov scored Tampa Bay's only goal in regulation to tie the game at 11:10 in the second period, then scored the clinching goal in the shootout. Steven Stamkos also scored in the shootout, while Andrei Vasilevskiy stopped attempts from Jack Eichel and Casey Mittelstadt after making 29 saves in regulation.
The Lightning entered the game averaging a league-best 3.9 goals per game. The Sabres held them to one goal by managing the puck to prevent chances on the rush and defending physically, clearing lanes for Hutton to see shots when the Lightning worked their way to high-danger areas.
"I just liked the desperation, urgency and the emotion that we brought to the game," Sabres coach Phil Housley said. "Guys were playing for one another. Our D-zone coverage and our rush coverage was really, really solid against a really talented hockey team."
The Sabres watched tape of their previous meetings with the Lightning on Thursday morning, one of which they won and two of which they led in the third period before falling late. In each case, the Lightning had brought the best out of the Sabres.
Their fourth meeting wrought similar intensity. Emotions boiled over late, with Jeff Skinner and Brayden Point dropping gloves in the third period and Rasmus Ristolainen drawing the ire of Kucherov, resulting in matching roughing minors for both players in overtime.
"We play with urgency," Evan Rodrigues said when asked how the Sabres have competed with the Lightning. "We respect their game - they're obviously a top team - and we play the right way, we defend properly, and we have a commitment to it. That's the way you have to play against every team in this league if you want to win some games here."
The Sabres will have to carry that same urgency into every game going forward, especially given the strength of their upcoming schedule. Four of their next five opponents occupy playoff spots in the Eastern Conference, with the fifth being a Philadelphia Flyers team that's fought its way into the hunt.
"I think it was great to see the way they responded," Housley said. "We were getting under some guys' skins and we competed hard. Every battle was a hard-fought battle. Again, we've got to continue to do that. We can't be satisfied.
"We got a huge point on the road against a very, very good hockey team that's been playing some excellent hockey. That's good. We've got to recognize how we have to play moving forward."