Hagelin's second goal of the series doubled the Rangers' lead midway through the second.
Carl Hagelin, Ryane Clowe, Anton Stralman, Rick Nash and Ryan Callahan also scored for New York.
Assists went to Carl Hagelin and Stepan, pushing New York's lead back to two goals.
At first glance, Hagelin seems a wisp, hardly built for the rigors of an NHL campaign.
New York took the lead again less than two minutes later on Hagelin's eighth goal.
The Rangers tied it at 1 when the surging Hagelin scored at 7:39 of the second.
However, Hagelin's pass went off the right skate of the Sabres' Adam Pardy and into the net.
Rather than turn pro, Hagelin elected instead to become the first Swedish-born recruit to play at Michigan.
Hagelin scored his first goal 31 seconds in and then made it 3-0 in the second period.
The battle between Mr Buchanan and pro-Perot supporters of rival nominee John Hagelin has split the party.
Hagelin has 15 days to appeal, but the money is likely to be long gone by then.
His clearing attempt was knocked down by New York forward Taylor Pyatt, who moved the puck to Hagelin.
One might not have thought that in 2007, when the Rangers used a sixth-round pick to draft Hagelin.
Rangers coach John Tortorella broke them up for more balance and moved Nash alongside Hagelin and Derek Stepan.
Ever since Hagelin joined the Rangers, head coach John Tortorella has been careful to temper his praise of him.
Notes: Hagelin had two goals and an assist in the Rangers' previous game.
Miller scored two goals on Thursday, and second-year forward Hagelin matched him Sunday.
"That's what we needed in the beginning, " Hagelin said of the secondary scoring.
Hagelin dropped the puck to Richards, who blasted a shot over Lehner's glove into the far side of the goal.
With Holtby well out of position, Hagelin's shot at a net guarded only by defenseman John Erskine was saved by Erskine.
Hagelin is also enjoying his time playing with Stepan, but thinks his teammate came in with plenty of innate hockey sense.
He also recorded three winning goals in that span while playing on a line with Callahan and fellow forward Carl Hagelin.
Carl Hagelin tied it for the Rangers in the second period after defenseman John Carlson put Washington ahead in the first.
Washington was outshot 13-9 in the second, but scored twice in the final 6:52 to get even after Hagelin made it 2-0.
From his first day at Michigan, Hagelin emerged as something of a legend for his performance in Berenson's infamously grueling conditioning drills.
Carl Hagelin scored for the second straight game, and Derek Stepan and Anton Stralman each added an unassisted goal for the Rangers.
Yet to this day, Eckert has never met or spoken with Hagelin.
Brad Richards and Hagelin staked the Rangers to a 2-0 lead, but goals by Mathieu Perreault and Troy Brouwer tied it for Washington.
"I think we played a great game, " said Rick Nash, who had an assist to set up Hagelin's goal and scored in the shootout.
All the young players who were supposed to be dynamite on the second line, like Carl Hagelin and Chris Kreider, have been anything but.
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