Alex DeBrincat made it 3-1 at 14:21 of the third after one-timing a cross-slot pass from Joseph.
"Too many penalties," DeBrincat said. "It's hard to get a flow when we're always in the box or they're in the box, for that matter. It's hard to get that 5-on-5 consistency, but I thought we did a good job sticking with it. One-goal game going into the third period, and we did a good job and stuck with it the whole game, so it's a good win for us."
Stutzle scored an empty-net goal with 41 seconds left for the 4-1 final.
"We did have chances," Sabres coach Don Granato said. "Unfortunately, we didn't convert. That's anybody's guess why not. We had a couple posts and crossbars, but that's the way it goes.
"We're in a little bit of a frustrating time with a lack of success recently. We have a young team that's going to go through it. We have to keep pushing."
NOTES: Comrie will "be out a little bit," Granato said. He will be reevaluated Thursday. … Sabres forward Zemgus Girgensons did not play in the third period due to an undisclosed injury and will be reevaluated. … Senators forward Claude Giroux's point streak ended at nine games. … Sanderson's nine assists are tied for the NHL lead among rookies with Arizona Coyotes forward Matias Maccelli.