The Sharks penalty ranked 14th of 16 playoff teams heading into the game (21-for-29, 72.4 percent).
"That was a game-changer," Sharks coach Peter DeBoer said. "We needed that. I think we talked going into the playoffs and after the first round (a seven-game win against the Vegas Golden Knights) that our special teams are going to have to win us games and ... I thought our penalty kill was a big part of the win tonight."
Thornton, who had a goal, an assist and was plus-3, said the Sharks felt the boost from killing Dillon's penalty.
"You felt kind of the spirit in here a little bit more, it was a four-minute penalty, that's tough for a high stick, but after that we kind of got our confidence off that kill and really went from there," he said.