Bruins right wing David Pastrnak, center, celebrates his first-period goal Thursday night against the New York Rangers. Adam Hunger/Associated Press

NEW YORK — The Bruins faced one of their toughest tests of the young season on Thursday and passed with flying colors.

Facing a surging, physical New York Rangers team that believes it’s a true contender in the Eastern Conference, the Bruins coughed up two one-goal leads but finally pulled away in the third period for a 5-2 win at Madison Square Garden.

In the third period, the Bruins outshot the Rangers 17-4.

The Bruins improved to 10-1 and Linus Ullmark stretched his record to 8-0.

In a wild third period, Charlie Coyle broke a 1-1 tie at 2:56, only to have the Bruins give up the equalizer just 48 seconds later.

On the go-ahead goal, Hampus Lindholm went behind the net and made a pretty pass to Coyle, who beat defenseman Jacob Trouba for position at the side of the crease and jammed the puck past goalie Igor Shesterkin.

The Rangers tied it less than a minute later. Brandon Carlo and Matt Grzelcyk gave Adam Fox a little too much space, and the terrific defenseman sniped a wrist shot over Ullmark’s shoulder.

But Trent Frederic gave the Bruins the lead again at 6:04, one-timing a Nick Foligno pass past Shesterkin from the left circle.

At 10:19, the Bruins finally stretched their lead to two goals off a nice rush. Pavel Zacha relayed a Taylor Hall feed to Jake DeBrusk, who buried a one-timer.

The Rangers pulled Shesterkin, but Lindholm clinched the win with an empty-netter.

The Bruins took a 1-0 lead at 12:53 of the first on David Pastrnak’s eighth goal of the season – one that reigning Vezina Trophy-winner Shesterkin would want back.

Pastrnak had taken a big hit from Ryan Lindgren earlier in the period and did not like it, earning two minutes in the box for a late hit that was called interference. Lindgren would later leave the game because of an upper body injury and did not return. It’s not clear if the hit had anything to do with the former Bruins farmhand’s injury.

When he came out of the box, Pastrnak looked determined to do some damage in his more customary manner.

On the scoring play, Pastrnak carried the puck down the left wing against Jimmy Vesey. He leaned into Vesey to give himself some space, but it looked like he was running out of room when he flipped a high backhander from the bottom outside of the circle. Shesterkin raised up to get it with his near shoulder and lifted the net, but not off its pegs. The puck somehow made it through.

“Surprising goal for me. I don’t score too many on the backhand. I felt like Patrick Kane for a minute,” Pastrnak told ESPN after the first period.

That was the only goal in what was a good period for the Bruins, who held a 11-4 shot advantage.

But the Rangers slowly started to get back in the game in the second period and eventually tied it at 10:21, with Vesey redeeming himself.

Ullmark had to make several Grade A stops early on, but he had little chance to stop Vesey, who tapped home Mika Zibanejad’s beautiful cross pass that got through defenseman Anton Stralman.

Then things got really nasty. Frederic carried the puck into the New York zone and got blown up on a hit by defenseman Braden Schneider. It was a clean hit, but it didn’t sit well with A.J. Greer or Frederic. Greer beat Frederic to Schneider, then Frederic went after Barclay Goodrow, and a pair of bouts took place about 3 feet away from each other. Greer wound up getting the instigator and the accompanying 17 minutes in penalties.

NOTES: Derek Forbort will be out 4-to-6 weeks after undergoing open reduction and internal fixation surgery on his right middle finger. Forbort, who had been one of the Bruins’ best defensemen in the first 10 games, was hurt when he took a puck off the hand in a 6-5 win in Pittsburgh on Tuesday.

Coach Jim Montgomery said Jeremy Swayman, who suffered an apparent knee injury on Tuesday, would be out “week to week,” though no specifics were given on the goalie’s injury.