Jeremy Swayman, Brandon Carlo

Bruins goaltender Jeremy Swayman is congratulated by defenseman Brandon Carlo after getting his second shutout in his nine NHL starts as Boston earned a 4-0 win against the New York Rangers. Elise Amendola/Associated Press

BOSTON — Patrice Bergeron scored in his fourth straight game, Jeremy Swayman needed only 15 saves for his second career shutout and the Boston Bruins beat the New York Rangers 4-0 on Thursday night.

Jake DeBrusk, Charlie McAvoy and Brandon Carlo also scored and Brad Marchand and David Krejci had two assists apiece to help the Bruins win for the fifth time in six games. The teams will meet again on Saturday in Boston.

The Rangers, in the midst of a tumultuous week that included the firing of the club’s president and general manager, were listless from the start and lost their fifth straight. New York had just four shots on goal in the first period and three in the second.

“We didn’t lay down. I know the shots were what they were and it looked ugly at times, but these guys competed,” Rangers Coach David Quinn said. “There’s a lot of good here right now. It’s just unfortunate that we’re in this position.”

Swayman, a former UMaine goalie, stayed sharp despite most of the action occurring at the other end of the ice until the third period.

“We did a real good job in front of our goaltender. We did not give up much tonight,” Boston Coach Bruce Cassidy said. “Obviously, we had a team come in here that went through an emotional process yesterday. But still, you’ve still got to play the game, and I thought we did a really good job in front of him.

Rangers goalie Igor Shesterkin had a much busier night, stopping 30 shots and preventing a larger rout.

Swayman, playing exactly a month after his NHL debut, won for the fifth time in his last six starts.

“He’s having a blast and he’s playing well,” McAvoy said. “Seeing his attitude, the way he does it and how he carries himself, he loves to have fun at the rink and it’s awesome and it’s contagious.”

The Bruins gave him a lead to work with 7:11 into the game when Marchand fed Bergeron from behind the net for a one-timer from the right circle.

Marchand picked up another assist on McAvoy’s power-play slap shot that put Boston up 2-0 with 1:25 left in the first period.

DeBrusk beat Shesterkin on a breakaway 14:01 into the second. It was just the fifth goal of the season for DeBrusk, who hadn’t scored since April 10.

Carlo hadn’t scored since Feb. 1, missing much of March and April because of injuries before returning to the lineup this week. He scored from a bad angle, skating with the puck down to the goal line and firing a shot toward the front of the net, where it deflected off Shesterkin’s right skate and into the net 1:07 into the third.

NOTES: The Rangers were without star center Artemi Panarin, who was injured during the chaos against Washington that ended his season. The Rangers were also without injured defensemen Jacob Trouba and Ryan Lindgren and forwards Chris Krieder and Brett Howden. … Left wing Pavel Buchnevich was out of the lineup, as he served a one-game suspension for cross-checking Washington’s Anthony Mantha on Wednesday night. … Bruins forward Charlie Coyle, who set out the third period Tuesday at New Jersey because of an undisclosed injury, was out of the lineup.

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