Brayden Point and Mitchell Chaffee scored for the Lightning (32-24-6), who have lost two in a row. Andrei Vasilevskiy made 20 saves.
"I thought we played pretty well until we took the penalties in the end," Tampa Bay coach Jon Cooper said. "Tip your hat, their goaltender played pretty well. He made some 10-bell saves when we probably could have put this game a little bit out of reach. He kept them in it, and they kept plugging away."
Lightning forward Brandon Hagel had his point streak end at 14 games (21 points; nine goals, 12 assists).
Point gave Tampa Bay a 1-0 lead on the power play at 8:12 of the first period after he made a strong move to the net past Sabres defenseman Connor Clifton and beat Luukkonen with the forehand. He extended his point streak to eight games (10 points; six goals, four assists).
"We need the points, so it's tough to lose the points," Point said. "I think we carried a lot of the play tonight. We did a lot of good things. Then we took a penalty and they scored on it, and took one in OT and they scored on it."