In the aftermath of the brawl, Tortorella could be seen yelling at the Flames' bench and Hartley.
"It's great that he [Tortorella] has our back," Sestito said.
Later in the period, Calgary's Mark Giordano punched Burrows in the face. Burrows was wearing a face mask to protect a broken jaw. It was his first game since Dec. 1.
Tortorella made no apologies for the lineup he started.
"I know the other guy across the bench," he said. "It's easy for people to say, 'Well, put the Sedins out there and it's deflated.' I can't put our players at risk like that.
"With the lineup that he had, I'm not going to put those types of players at risk, and that's what ensued. I'm not proud of it. I've apologized to every one of the players involved in it. I don't feel great about it at all."
Hartley also defended his starting lineup.
"Those guys are playing well for us," he said. "They got a goal last game. We're not scoring many goals. We had zero intentions there.
"As far as I know, they were the home team. They had the luxury to put whoever they wanted on the ice."
The teams combined for 188 penalty minutes in the first period -- 142 penalty minutes in the first five minutes of the game and smaller skirmishes throughout the opening period. Calgary's Shane O'Brien and Vancouver's Zack Kassian each received 10-minute misconducts later in the period. A total of 204 penalty minutes were logged Saturday night.
Tortorella declined to answer questions about potential disciplinary actions, although he likely will receive either a hefty fine, a suspension or both.
The fiery coach has been fined multiple times for some particularly colorful postgame tirades. He has was suspended in 2009, while with the New York Rangers, for throwing a water bottle at a fan during a game against the Washington Capitals.
This was not the first time Tortorella encountered a situation like Saturday night. He blasted Devils coach Pete DeBoer from the bench after DeBoer started his fourth line against Tortorella's Rangers in 2012, an uncannily similar incident in which Tortorella matched with his tough guys -- having rugged defenseman Stu Bickel take the opening draw -- and a line brawl ensued.
ESPNNewYork.com's Katie Strang and The Associated Press contributed to this report.