SUNRISE, Fla. — Jeremy Swayman said the series would return to Boston. And he backed up that claim in a big way.

Swayman made 28 saves, Charlie McAvoy added to the list of disputed goals in this matchup with the go-ahead score and the Boston Bruins staved off elimination by beating the Florida Panthers 2-1 in Game 5 of their Stanley Cup playoff series Tuesday night.

The biggest stop of Swayman’s night might have been his last: He stoned Florida’s Sam Reinhart from close range with about 8 seconds left, and the Bruins — just as he vowed — left Florida winners.

“We have a goaltender that’s extremely confident,” Bruins coach Jim Montgomery said. “His swagger gives confidence.”

Morgan Geekie also scored for the Bruins, who improved to 2-0 in elimination games this season — they also won Game 7 over Toronto in Round 1 — and finally found a way to hold the Panthers’ offense in check.

Reinhart scored for Florida, and Sergei Bobrovsky stopped 26 shots. The Panthers had just four shots in the first, then got 25 to Swayman in the final 40 minutes.

“We had our missed opportunities,” Panthers coach Paul Maurice said. “There’s a losing coach’s line: ‘We had our chances.’ I didn’t like our game. But I like the fact that from where we were in the first, we got into a much, much better place in the second and third.”

Florida — which saw its series lead cut to 3-2 — had 15 goals on 107 shots in Games 2, 3 and 4 combined, all of them Panthers wins. But on Tuesday, the Panthers were held to 29 shots and Swayman looked in total control the whole way.

Game 6 is in Boston on Friday. Game 7, if necessary, would be back in Florida on Sunday.

“The reality is that we’re going to go to Florida and we’re going to play the same game and we’re going to get it done,” Swayman said after Game 4. “I have no doubt in this group. And we have a lot of confidence and a lot of motivation to bring it back to Boston.”

It’s going back to Boston.

“I just can’t thank my mentors enough for showing me the way and replacing that word ‘nervous’ with ‘excited’ and just being me and embracing moments,” Swayman said after Game 5. “That’s when I find the most enjoyment, truly living it to the absolute fullest. And I couldn’t be happier.”

Bobrovsky was pulled with 3:05 left, Florida going 6-on-5 in an effort to tie the game, but the Panthers managed to get only three pucks to Swayman the rest of the way.

The Bruins played the second straight game without their captain and leading scorer Brad Marchand, who hasn’t been on the ice since late in the second period of Game 3 because of what Boston is calling an upper-body injury. He was hit by Florida’s Sam Bennett and wound up leaving that game, a play that the Bruins said was dirty and has only added to the intensity of the series.

Marchand was at the game, his jersey was hanging in his locker and he gave his team pep talks between periods.

“We know what he means to this group,” McAvoy said. “We didn’t say die. We wanted to see this thing go back to Boston and give him a chance to get right and hopefully be back.”

Down 1-0 in the second, Maurice gathered his team around the Florida bench during a TV timeout and used that stoppage in play to get some thoughts out — at high volume. Red-faced by the time his rant was over, Maurice was pointing animatedly and had the attention of everyone from players to assistant coaches to even the team’s equipment staff.

“I thought they needed some profanity in their life, and I brought some,” Maurice said.

Message received. Only 11 seconds after play resumed, Reinhart lifted a rebound past Swayman to tie the game at 1-1.

“It seemed to turn our game around a little bit,” Reinhart said of the Maurice rant.

But Boston had the lead again when the second period ended, after McAvoy scored a goal midway through the frame where Florida — just like the Bruins did on a big goal for the Panthers in Game 4 — claimed interference. Boston’s Danton Heinen made contact with Bobrovsky with his stick, but NHL officials in Toronto said it wasn’t enough to take the goal off the board.

“Tonight was our best game in the series,” Montgomery said.