COLUMBUS -- John Tortorella took it all in as streamers fell from the rafters and fans inside Nationwide Arena celebrated the Columbus Blue Jackets' first playoff series victory in their history.

"I couldn't be happier," the Blue Jackets coach said after a 7-3 win against the Tampa Bay Lighting in Game 4 wrapped up a historic sweep in the Eastern Conference First Round on Tuesday.

It was arguably Tortorella's proudest moment and biggest accomplishment in hockey since winning the Stanley Cup with the Lightning 15 years ago. The four playoff victories in the past seven days by the Blue Jackets are one fewer than the total number of postseason games they had won since joining the NHL in the 2000-01 season.

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Tortorella and the Blue Jackets did it in historic fashion too, becoming the first team in NHL history to have a first-round sweep of the team that had the best record in the regular season. Tampa Bay, which won its only Stanley Cup with Tortorella as coach in 2004, tied an NHL record with 62 wins in the regular season. The Blue Jackets didn't let them get another.

"I've been fortunate enough to be in some pretty big games and loud buildings. That building tonight, that was just unbelievable," Tortorella said.

He talked as his players congratulated themselves in their dressing room while the 19,328 fans who packed the arena, the third-largest crowd in the history of the Blue Jackets, were pouring onto the streets in the arena district, celebrating as if this was bigger than a first-round win.

"I'm thrilled for not only the people that have followed the team but also the people in the organization here too," Tortorella said. "Just remember, it's one round and we're thinking about other things as we go along here. But I know that's a burden that's been here, not winning a round in the organization. I'm thrilled for the people that have grinded through this and get to have a little bit of excitement here as we get to play our second round."

The Blue Jackets will face the Toronto Maple Leafs or the Boston Bruins in the Eastern Conference Second Round; Toronto leads the best-of-7 series 2-1 heading into Game 4 at Scotiabank Arena on Wednesday (7 p.m. ET; NBCSN, CBC, TVAS, NESN).

Imagine that; the Blue Jackets waiting to find out who they will play next in the playoffs.

Tortorella arrived here seven games into the 2015-16 season as the replacement for Todd Richards, who was on the Lightning bench for this series as an assistant to coach Jon Cooper. Tortorella has taken the Blue Jackets to the playoffs for three straight seasons, giving the fans something to celebrate this season.

"I appreciate them," Tortorella said. "Just being out in the community, the people have been fantastic. Since I have been here, they have just been fantastic. I'm really thrilled for them that they get to taste this."

Video: Blue Jackets sweep Lightning for first series win

Tortorella is also thrilled for his players, many of whom have never been to the second round.

Goalie Sergei Bobrovsky, injured defenseman Adam McQuaid, and forwards Brandon Dubinsky, Ryan Dzingel and Riley Nash are the only players on Columbus' roster to have played a game past the first round.

"I was asked by [NBC broadcaster] Pierre [McGuire] during a timeout as far as do you tell your players to keep their composure," Tortorella said. "Not for a second. I mean as far as not being too excited, and I told him, 'No, I want them to enjoy this.' We were composed in how we play, I wasn't worried about that. I want them to enjoy this to see what the building is.

"I want them to experience it and have fun doing it."

He loves how they did it, with will and determination, especially after falling behind 3-0 in the first period of Game 1.

"I'm standing at the bench as the games we're playing and talking about some backchecking things we needed to do to play against this team, and I'm listening to the bench when some guys aren't doing it and I don't have to say a word because it's coming from them," Tortorella said. "I looked at [assistant Brad Larsen] in Game 3, I heard people screaming at one another to backcheck.

"For a coach, it's really cool to see that, because it's usually the coach doing all the yelling about that. You could see that they had an opportunity against a really good team and they didn't want to see this go by."

Tortorella said he feels especially good for Bobrovsky because he has been dogged in the past for being a goalie who couldn't win in the playoffs. Bobrovsky went 4-0 with a 2.01 goals-against average and .932 save percentage in the series; he had been 5-14 with a 3.49 GAA and .891 save percentage in his previous 24 playoff games.

"I'm happy for him," Tortorella said. "He's not crazy about what I have talked about with some of the situations he's gone through, but it's my job to hold people accountable. I'm thrilled that he's answering. He's answering. He's got a bit of a burr, and that's a pretty good thing for an athlete to have."

The Blue Jackets will enjoy some well-earned days off Wednesday and Thursday. They'll be back at the rink Friday, together again to begin preparations for the second round.

"It's only one round," Tortorella said.