Thompson kept the game tied with a glove save against Charlie McAvoy's wrist shot from the right face-off circle 55 seconds into overtime on a 2-on-1 rush.
"To be honest, I thought he was going blocker," Thompson said. "And then he, last second, I was able to flick my hand up. It always feels good being able to make those saves, and I'm already in the game. It gets you more into it, for sure."
Cotter gave the Golden Knights a 1-0 lead at 1:36 of the first period. William Karlsson fed Cotter in the slot from behind the net. It was Cotter's first point in 11 games (Nov. 12).
"That many games in a row without a point is unacceptable," Cotter said. "I mean, it's going to happen; it's my first year. But if I play my game, I'm sure I should be able to get points, whether it's a weird tip-in or battle in front."
Jonathan Marchessault made it 2-0 at 5:04, picking off a David Pastrnak breakout pass deep in the Bruins zone and rebounding in Swayman's pad save from his initial shot.
"I just saw that Pastrnak was looking at the [defensemen] sometimes on the breakout," Marchessault said. "I was just trying to cut that play off, and no, I'm just pretty disappointed I missed my first shot there."