NEW YORK -- The scoreboard showed that the Boston Bruins were only even with the New York Rangers after the first period. In reality, Tuukka Rask had already won the game for the Atlantic Division leaders.
Rask made 19 saves in a one-sided opening period, and defenseman Dougie Hamilton had a goal and two assists to lift the Bruins to a 6-3 victory over the Rangers on Sunday night.
New York jumped ahead 14-1 in shots and took a 1-0 lead it couldn't hold. The Bruins skated off in a tie despite being badly outshot.
"We were stuck in quicksand. We didn't do anything there, just gave them all kinds of chances," Rask said. "Then we finally got that goal, got some life, and the last eight minutes in the first we played good.
"You're outshot 20-9 and it's 1-1 so you're somewhat relieved. We got better and got the lead and never gave it up."
Rask finished with 39 saves. He outdueled New York's Henrik Lundqvist, who stopped 27 shots on his 32nd birthday but lost for the second straight day.
Lundqvist allowed a season-high tying six goals.
"Painful. Extremely painful," Lundqvist said. "I thought we played pretty good. They worked hard, but their goals were unbelievable with the bounces they got -- a couple of deflections and a post and in."
The Bruins improved to 9-2-3 in their last 14 games and earned their first season-sweep of New York in 31 years.
Rask made 43 saves in a 2-1 win over the Rangers on Nov. 19 in Boston's previous visit to Madison Square Garden.
"I thought we started to get a little bit better in the second half of the first (period)," Bruins coach Claude Julien said. "We slowly got ourselves back in the game, but were much better in the second and the third.
"We got mad enough after the first 10 minutes that we reacted to doing something. That was huge. We just needed to get over that hump. Once we scored that first goal, it just seemed like everybody relaxed and we got better."
The Rangers fell one point behind second-place Philadelphia -- which beat New York 4-2 on Saturday. They lead fourth-place Washington by one point in the Metropolitan Division. All three teams have 20 games remaining.
Lundqvist has allowed nine goals in two games since returning from the Olympics.
"I don't think that was a game that dictated the score," said Rangers captain Ryan Callahan, who could be traded before New York's next game on Wednesday. "I thought we had some good minutes."
Boston, which didn't have a power play, increased its lead to 5-2 in the third period on a pair of goals by Gregory Campbell -- first short-handed at 9:04 and then at even strength with 6:34 left. Milan Lucic finished the scoring with 1:36 remaining.
The Bruins have received an NHL-low 176 power plays this season.
"They could've mixed one in, but it seems to go the other way for us all the time," Rask said.
Jarome Iginla scored in the first period, and Hamilton and Carl Soderberg connected in the second with assists from Hamilton. Boston won all three games from the Rangers for the first time since the 1982-83 season.
Iginla began to change momentum when he scored with 1:53 left in the first.
"They played yesterday, too, and it should've been a pretty even start," Rask said of the Rangers. "We just weren't ready. We weren't skating and it was pretty ugly there. I was a little surprised."
The Bruins came out for the second re-energized. Unlike New York, however, Boston capitalized on two early chances and surged ahead 3-1 just 9:34 in.
Iginla helped pushed Boston in front when he freed a puck from the left-wing boards. The puck found its way to Hamilton, who scored his seventh at 4:04.
Soderberg stretched the lead to 3-1 just 5:30 later when he gathered the rebound of Loui Eriksson's hard shot, shifted the puck from backhand to forehand and scored his 10th goal. Hamilton earned his second assist of the night.
The Rangers got back within a goal when Richards got a puck past Rask with 3:07 left. Richards patiently stopped at the blue line and stayed onside while awaiting a pass from Callahan. Richards took the puck into the right circle and snapped a drive that sailed wide past Rask and into the open left side for his 16th goal.
Boston held a 14-12 edge in shots in the second, but again found a way to make the most of them.
"It's a great win when you score six goals on a good goalie like that," Rask said.
New York grabbed a 1-0 lead when Miller converted a turnover at the blue line into a breakaway for his third goal of the season on the Rangers' third shot. Rask then stopped the next 17 in the period -- including difficult chances in close by Callahan and Chris Kreider.
The Bruins, who lost to Washington on Saturday, are 8-2 in the second game of back-to-backs. ... Hamilton had three career two-point games, none this season. ... Rangers RW Derek Dorsett was scratched one day after returning to the lineup following an 18-game absence caused by a broken leg. Dominic Moore took his place.