Patrice Bergeron, right, is congratulated by Jake DeBrusk after scoring the first goal of his three goals Thursday night in a 5-0 win over the Buffalo Sabres at TD Garden. Charles Krupa/Associated Press

BOSTON — Patrice Bergeron scored three times, reaching 400 goals in his NHL career. David Pastrnak tallied his 40th of the season, snapping Boston’s 0-for-39 power-play slump. And Linus Ullmark recorded his first shutout as a Bruin.

“It’s a pretty happy room in there. Even Frank Sinatra playing, if you can believe that,” Bruins Coach Bruce Cassidy said after his team beat the Buffalo Sabres 5-0 on Thursday night. “A lot of positives.”

Bergeron recorded his eighth career hat trick, and Pastrnak scored Boston’s first power-play goal in almost four weeks as the Bruins won their final home game of the season. Ullmark made 37 saves against his former team as he tries to win the job as No. 1 goaltender for the playoffs.

“I’m focused for what’s to come,” said the goalie, who shared the traditional postgame hug with rookie Jeremy Swayman as the fans cheered. “Regular season doesn’t mean anything. We’re heading into the playoffs.”

It was already 4-0 when Bergeron gathered in a pass from Charlie McAvoy and wristed it into the net with 2:13 remaining. Hats came flying over the glass, and the Bruins hugged their captain, jumping up and down on their skates.

It was the 100th hat trick in the NHL this season. Bergeron is the fourth Bruin to score 400 goals, joining Johnny Bucyk (545), Phil Esposito (459) and Rick Middleton (402).

“It is special, and one of the things that is special is that … it’s been a great ride with one organization. It’s something that doesn’t happen often. I’m proud of that,” Bergeron said. “To share that with them and for them to have that reaction was great, was special and it was very much appreciated.”

Bergeron and Mark Messier are the only players to complete a hat trick with their 400th goal, according to STATS.

Dustin Tokarski stopped 27 shots for the Sabres, who will miss the playoffs for the 11th straight season.

The Bruins failed to convert on their first three power plays Thursday, making it 39 in a row since April 2. Then they scored on two straight, with Pastrnak hitting the 40-goal mark for the second time. Only Phil Esposito (7), Rick Middleton (5), Cam Neely (4) and Ken Hodge (3) have more 40-goal seasons with the Bruins.

Taylor Hall made it it 4-0 after the delay-of-game penalty assessed on the Sabres for unsuccessfully challenging Pastrnak’s goal.

“We didn’t need the goals, but we don’t need to be talking about it forever, so it’s good to get ’em,” Cassidy said. “You could sense it was happening. So it was going to come sooner or later.”

7TH MAN

Goalie Jeremy Swayman won the Bruins 7th Player Award, which was presented before the game.

Swayman, 23, has a 20-11-3 record while posting a 2.34 goals-against average. He leads all rookies in GAA, save percentage (.915), wins and shutouts (3).

Ullmark, who is 25-10-2 with a 2.51 GAA, appears to have earned the starting position going into the playoffs. It would be his postseason debut; Swayman appeared in one game in relief of Tuukka Rask last year.

Coach Bruce Cassidy said earlier Thursday that he wasn’t against using both.

“It’s going to be a decision in the moment, I guess, is the easiest way to say it,” he said. “It could go one way or the other, to be perfectly honest.”

FOND FAREWELLS

The Bruins said goodbye to head athletic trainer Don DelNegro, who is retiring after 29 years with the team. There was a compilation of good luck videos shown on the scoreboard, and another video showed the players presenting him with a golf cart as a retirement gift.

After the game, the team posed for a picture with DelNegro at center ice and then he walked through the players to the bench.