"That was big on him and sets the tone for the rest of the game," Tage Thompson said. "It allowed us to just kind of settle in and get back to our game."
Added Granato: "He wanted to do it for his team and his teammates. He's in a new place, new fans, new environment and he went into that and I don't think he was thinking about himself one bit."
The Sabres acquired Stillman and forward Jordan Greenway in the days and hours leading up to Friday's trade deadline in part to add a pair of physical presences to their roster. Greenway was unavailable to play against the Lightning because of travel delays, but Stillman was back in the lineup after recording six hits in his debut against the Bruins.
Stillman's response in the second period was a microcosm of the Sabres' afternoon against the three-time reigning Eastern Conference champions. The Sabres had plenty thrown at them - an early deficit, multiple post-whistle scrums, six minor penalties - but stayed the course through it all.
Tage Thompson, Vinnie Hinostroza, Tyson Jost, Jack Quinn, and Jeff Skinner all scored goals - three of which came during the second period, which began with the two teams tied 1-1. Rasmus Dahlin added an assist in his return from a three-game absence stemming from a lower-body injury.
Eric Comrie made 31 saves to win his fourth straight start.
"There was a lot to fight through to make sure we were steadfast and (played) how we wanted to play with pace and pressure, and a lot of things that could've caused ups and downs and distractions," Granato said.
"I commend our guys staying very dialed in. Because we needed that win. And I think our room knew we needed that win."
The victory snapped a brief two-game losing streak for the Sabres. It was the fourth straight loss for the Lightning, who benched three of their forwards in Steven Stamkos, Brayden Point, and Nikita Kucherov during the third period.
"I think we needed a big response after our last game against Boston," Thompson said. "I think we were on our heels a little bit last game and I think tonight coming in we just wanted to make sure that no matter what happened, whether they get a push or not, we're stepping on the gas the whole time."