Before the game, Senators coach Guy Boucher said forward Bobby Ryan would be out indefinitely because of an injury to his right index finger. Top-six forwards Mike Hoffman and Stone each left the game Sunday, and forward Tommy Wingels also left in the third period after he was hit by Byfuglien.
Hoffman left after the first period because of a lower-body injury, and Stone left at 6:42 of the third period after he was hit by Jets defenseman Jacob Trouba, who was assessed a minor penalty for an illegal check to the head.
"Right now, it looks like a disaster," Boucher said of the Senators' injury situation. "We'll see [Monday]. Maybe the disaster is not as bad as we think. Right now, I'd rather be ready for anything."
The Jets are 2-0-1 on their four-game road trip, which wraps up Tuesday against the Toronto Maple Leafs, their final game before a six-day break.
"I liked it a lot," Hellebuyck said. "We were doing the little things right again. I know I talk about that a lot, but it really makes a difference in the game. Getting sticks on pucks when they are about to shoot, it really changes my game. It also helps that we blocked a lot of shots tonight and a lot of key shots. You can go around the room and find a couple of bruises on each guy."