Sam Reinhart scored twice for the Sabres (9-5-2), who are winless in their past four games (0-3-1).
"I think for a lot of the game, we played the way we wanted to," Reinhart said, "I think there was just a couple of instances when our tempo slowed down, we were a little disconnected and that led to their opportunities. For the most part, I think when we were connected and supporting each other, we created a lot of chances for ourselves."
Kucherov scored on a one-timer at 3:19 of the first period for a 1-0 lead.
Hedman assisted on Killorn's goal at 16:14 to make it 2-0. He played give-and-go with Steven Stamkos on the power play before taking a slap shot that was deflected by Killorn.
"Just really happy that not only he plays well in the game, he gets a point and the team wins," Lightning coach Jon Cooper said of Hedman. "It's a little hat trick for [Hedman]."
Reinhart made it 2-1 with 4:17 left in the second period on a deflection. The goal initially was disallowed because the referee ruled it was played by a high stick, but the call was overturned after video review.