The Sabres played with five defensemen after Owen Power sustained a lower-body injury before the game.
"It was maybe 10 minutes before warmup; he did something in his dynamic warmup pregame," Granato said. "It's a lower-body injury. We'll know more tomorrow, but he was in no spot to play, unfortunately. We had no option. We had no room on our active roster even, with [Jacob] Bryson being day to day, [Kyle] Okposo being day to day. There was nobody. Nothing we can do.
"Even if we could call a guy up, we couldn't call the guy up because we didn't have any definitive information on Owen, obviously, and two guys that are on the cusp of going in but couldn't tonight. So, tough situation."
Thompson gave Buffalo a 1-0 lead just 54 seconds into the game when he took a pass in the slot from Casey Mittelstadt and stuffed a shot past Georgiev for his 10th goal in seven games.
"The first goal is always big in this league, it just is, and what a play," Granato said. "I thought a lot of calm, a lot of confidence, a lot of poise to set that goal up and really set a tone by Middlestadt, Thompson, and Tuch."
Tuch scored his 15th of the season on a rebound of Dahlin's shot from the point for a power-play goal at 7:08 to make it 2-0.
Dahlin gave the Sabres a 3-0 lead at 17:11 of the second period with a wrist shot from between the face-off circles.
"I just put my head down and shot as hard as I could, so I was happy it went in," Dahlin said. "We got a really nice 3-0 lead, and we did a really good job closing the game. We kept the tempo, kept it hard."