WASHINGTON -- Five months ago, Washington Capitals rookie center Evgeny Kuznetsov had trouble staying in the lineup. On Monday night, he became a Game 7 hero.

Selected by Washington in the first round of the 2010 draft, Kuznetsov proved to be the Capitals' secret weapon against the New York Islanders, scoring a team-high three times in the seven-game series, including Monday night's game-winner in a 2-1 decision.

After the teams traded goals in a tense decisive game, Kuznetsov weaved through two Islanders defenders before ripping a wrist shot over New York goaltender Jaroslav Halak with 7:18 remaining in regulation, giving the Capitals a hard-fought, 4-3 series victory.

The Capitals earned the right to face the New York Rangers in the playoffs for the third time in four years. New York eliminated Washington in seven games in 2012 and 2013. Game 1 of the Eastern Conference semifinal series is expected to take place Thursday night at Madison Square Garden.

Right winger Joel Ward also scored for the Capitals, while center Frans Nielsen scored the lone goal for New York.

Outshot and outplayed through two periods, the Islanders tied the score with 3:13 gone in the third period when Nielsen took a pass from Thomas Hickey, fought through a stick check by Washington right winger Jason Chimera and snapped a shot that somehow found its way through the legs of Capitals goaltender Braden Holtby.

Nielsen's goal was his first in 13 career playoff games, and it quieted a sellout crowd anxious to celebrate its first Game 7 win at home since 2009.

Washington had several chances to restore the lead, but Halak was strong between the pipes, stopping right winger Troy Brouwer from the high slot.

The teams appeared to be heading to overtime for the third time in the series until Kuznetsov worked his magic.

The loss ended a remarkable run by the Islanders, who were forced to play their final two games of the series with little-used defensemen Scott Mayfield and Matt Donovan.

The Capitals dominated the Islanders through two periods, outshooting them 21-7, but they didn't break through on the scoreboard until 1:25 remained in the second period.

Halak appeared to lose sight of a long point shot by Capitals defenseman Brooks Orpik and could not control the rebound. Ward, who was parked in the crease, pitch-forked the puck under the prone Halak for his first goal of the 2015 playoffs.

Ward, who now has 12 goals and 30 points in 46 playoff games, reacted with two leaps into air before being congratulated by his teammates.

Seconds later, Holtby flashed out his right pad to stop a shot by New York defenseman Johnny Boychuk.

Holtby finished with 10 saves. Halak stopped 24 of the 26 shots he faced.

NOTES: Capitals LW Curtis Glencross returned to the lineup after sitting out Games 4, 5 and 6 as a healthy scratch. He played on the fourth line with C Brooks Laich and RW Tom Wilson. ... Capitals C Eric Fehr (upper body) skated Monday, with hopes of playing in Round 2. ... The Islanders went with the same lineup used in their 3-1 win in Game 6, which meant a third defense pairing of Matt Donovan and Scott Mayfield, who entered the playoffs with no postseason experience. Islanders G Jaroslav Halak entered Game 7 with a 6-1 record in elimination games, with a 1.72 goals-against average and .956 save percentage. ... Seventeen Capitals entered the game with Game 7 experience; the Islanders had five.