The Sabres celebrate one of their six goals on Sunday at TD Garden. A do-or-die Game 5 for the Bruins is tonight in Buffalo. (AP photo)

The Buffalo Sabres have shed the burden of a 14-year absence from the Stanley Cup playoffs that set a dubious NHL record and surged toward their next big thing.

Beat the Boston Bruins at home in Game 5 tonight (7:30, TNT, NESN), and the Sabres will skate in the second round for the first time since 2007.

“You can expect this to be the hardest game that we’re going to have to play short-term here, because they’re in the nothing-to-lose-and-everything-to-gain category,” said Sabres coach Lindy Ruff, whose first stint with the team was a 15-year run that included the most recent postseason appearance and series victory — plus four trips to the conference finals and one Stanley Cup finals berth.

The Bruins, behind first-year coach Marco Sturm, are reeling from a 6-1 drubbing they took on Sunday to fall behind 3-1.

“They know that if they don’t put whatever they can put into the game,” Ruff said, “they’re done.”

The Bruins lost their cool during their Game 4 meltdown. Defenseman Nikita Zadorov received a $5,000 fine from the league on Monday for cross-checking Sabres defenseman Rasmus Dahlin. Goalie Jeremy Swayman shouted at his own bench as he skated off after being pulled from the game.

“We have an extremely high competitive group. We all have a standard that we all carry ourselves to, and it wasn’t met. So that was just emotion,” Swayman told reporters. “It’s moved on now, and we have a job to do going into Buffalo.”

The Sabres can’t wait to take the ice in front of a fired-up crowd.

“When I came in last season, there was lots of talk of, ‘This is a hockey city, not a football city,’ and that was pretty hard to believe as an outsider coming in. You can see the passion for the Bills and just everything around that,” Sabres left wing Beck Malenstyn said. “But then I think throughout this year, we’ve slowly grown to see just how supportive and passionate this fan base is.”