Vasilevskiy now has six shutouts in series-clinching wins, the most in Stanley Cup playoffs history.
"Nothing special really", he said. "I think the way the whole team plays in those games, the whole series, constant blocked shots, sacrifices, the boys clearly breaking bones to stop the puck.
"Such a great effort by everybody on our team. Obviously, it's not just me. I am just trying to do my job the best that I can."
The Lightning have now won ten straight playoff series, joining the New York Islanders, who won 19 in a row from 1980-83 and the Montreal Canadiens, who had separate streaks of 13 and ten as the only teams to win ten or more consecutive playoff series.
"To sit here and think we're in the (same) breath of the greatest teams that have played this game and the amount, because that's when you're really measured", said coach Jon Cooper.
"What do you do in the playoffs, and to win ten series in a row, and what does that put us top three all-time."
"It's a special group, no doubt", said captain Steven Stamkos. "The beauty of the group is we're not satisfied. We want 12 straight [series]."
Pat Maroon and Ondrej Palat scored for the Lightning.
"It's special to be a part of this group", said forward Alex Killorn. "Like I said with 'Vasy', I think there's a lot of players on this team that will go down as some pretty good players, Hall of Fame players. So I'm just happy to be a part of it, to be honest."
Sergei Bobrovsky made 23 saves for Florida, who were shut out for the first time in the playoffs.
"I thought it was the best game we played as a 60-minute game", said coach Andrew Brunette. "Looked like us. I'm not sure if our backs were that far off the wall and there was no pressure, but we played like we played all year tonight.
"That wasn't always the case in the other nine playoff games, where we showed flashes of it, but the 60-minute game at the pace that looked like us."
Story of the game
Neither team scored in the first two periods, but Tampa Bay had two goals in the second period overturned on a challenge.
Killorn appeared to scored on a deflection, but Brunette challenged for a missed game stoppage, and the call was reversed after a video review.
Nikita Kucherov then scored from the left circle off a face-off win by Anthony Cirelli, but that was also called back after it was determined that Cirelli made a hand pass to get the puck to Kucherov.
'These goals are coming off the board, and then even the poot puck rolls on [Palat] at the end and you're like 'Oh my gosh, now we got to kill a penalty on this with two and a half minutes left", Cooper said.
"You make your own breaks, and the guys did that and literally, if that last penalty kill didn't personify what's gone on in our playoffs here, nothing does, and incredible stuff to watch."
Maroon got Tampa Bay on the board 6:16 into the third as he batted in a point shot taken by Zach Bogosian that rolled behind Bobrovsky and in.
"We were in a good position going into the third period, a 0-0 game", he said. "We still had an opportunity to win, and we just had to find a way to squeak one by, and we did.
"Obviously it was an ugly goal, but that's playoff hockey for you."
Palat scored an empty-netter with 33 seconds remaining after just getting out of the penalty box.
"Tonight, I thought we did a really good job of enforcing the game plan that we set to for tonight", said Florida defenseman Aaron Ekblad. "Obviously, it just wasn't enough. We got our chances. We just didn't capitalize on those scoring chances that are so dire.
"It's a tough pill to swallow. Getting swept is tough. It hurts. It stings. There's no doubt about it."
Florida didn't convert on any of their three power-play chances and were just 1 for 31 in the playoffs. They scored just three times in the series after leading the NHL with 337 in the regular season.
"They blocked shots", captain Aleksandar Barkov said. "They play really desperate defense. They play really well, so it's hard to get there. But like I said, we could have done a lot of things differently, but our effort was there every game."