Ondrej Palat had a goal and an assist after scoring 4:40 into overtime of a 4-3 win in Game 2 on Tuesday, Alex Killorn had two goals and an assist, and Andrei Vasilevskiy made 23 saves for the Lightning, the No. 2 seed in the East.
Kucherov had a goal and three assists to tie Vincent Lecavalier, Tyler Johnson and Brayden Point for most points in a playoff game in Lightning history.
"Come on, let's be honest, this is an aberration," Lightning coach Jon Cooper said, referring to the final score. "This doesn't happen in playoff hockey. They're the Presidents' Trophy champions. You turn the page on this one just like you turn the page on an overtime thriller. You can't hang your hat on that one.
"When a team has a clunker, you can't hang your hat on that one either. They're both just one win, and we're only halfway there. It's a funny game. You can't ride the emotions too high or too low."
WATCH: [All Lightning vs. Bruins highlights]
Dan Vladar relieved Jaroslav Halak to make 12 saves in his
NHL debut for Boston
, the No. 4 seed. Halak was pulled at 11:18 of the second period after making 12 saves on 16 shots after making 36 saves on Tuesday.
Game 4 of the best-of-7 series, scheduled for Friday, was
postponed
and will be played Saturday (Noon ET; NBC, SN, TVAS) in Toronto, the East hub city.
"It's over. We're going to focus on Game 4," Bruins coach Bruce Cassidy said. "A loss is a loss. They're up 2-1. I think we've got a good group in there. I know we've got a good group in there. They're resilient. So like I said, we'll lick our wounds tomorrow and get away from the rink, and get ready for Game 4."
Teams that win Game 3 after a Stanley Cup Playoff series is tied are 218-107 (67 percent) winning a best-of-7 series, including 3-1 this postseason.
"We are going to have to move on from this game," Bruins defenseman Zdeno Chara said. "Obviously, not our best game. We realize that was one of those games that nobody wants to look at, but definitely something we have to move forward from and get ready for the next one."