NEW YORK -- As the New York Rangers soared through a strong regular season, Filip Chytil endured his share of frustrating moments.

Now the same shots Chytil often saw fail to become goals are getting past goaltenders on a regular basis.

Chytil scored the tiebreaking goal with 9:51 remaining in the second period and added his second goal of the game nearly six minutes later as the New York Rangers pulled away for a 6-2 victory over the Tampa Bay Lightning on Wednesday in Game 1 of the Eastern Conference finals.

After never taking a series lead in their wins over the Pittsburgh Penguins and Carolina Hurricanes, the Rangers can take a 2-0 series lead on Friday thanks to Chytil's third straight game with a goal and second multi-goal game in that span.

Chytil scored his sixth and seventh goals of the postseason. He is one goal shy of matching his total from 67 regular-season games, when he scored just twice in his final 24 games.

"He works hard, he competes hard and he's deserving of what he's getting right now because he's stepping his game up," New York coach Gerard Gallant said.

Chytil, 22, has the second-longest goal-scoring streak in team history before the age of 23, one behind Alex Kovalev, who had a four-game run in 1994. His five goals in a three-game span are tied with Mike Gartner (1990) and Pentti Lund (1950) for the team's postseason record.

"It's fun to see, and Filip is unbelievable the way he's using his skating ability," New York's Mika Zibanejad said.

Chytil produced his latest goals by finishing off one-timers to give the Rangers a 4-2 lead through 40 minutes.

Chytil made it 3-2 after Kaapo Kakko sent him a pass from behind the net. The center leaned into a shot from the high slot that sailed into the right corner of the net.

Then Chytil scored again when the Rangers maintained possession in the offensive zone for well over a minute by blasting a shot from the right faceoff circle to beat Tampa Bay goalie Andrei Vasilevskiy.

"There were tough moments, so many chances when I couldn't put it in the net," Chytil said. "Maybe the hockey wasn't that bad, but when you're not putting the puck in the net, you're not helping the team that much.

"Now it's finally going in, I'm so happy that I can help the team like this."

New York's Chris Kreider scored 71 seconds in, and Frank Vatrano scored 7:50 into the second period. Artemi Panarin tallied 30 seconds into the third, and Zibanejad scored a power-play goal 6:06 into the third as the Rangers won their team-record seventh straight postseason home game.

Steven Stamkos and Ondrej Palat scored for Tampa Bay, which saw its six-game winning streak end following an eight-day layoff.

"Certainly not our best game," Stamkos said. "They're a team that has some really good players, and if you give them chances, they're going to bury them."

New York's Igor Shesterkin made 37 saves and won for the eighth time in 11 games since being pulled in Game 4 against Pittsburgh. Shesterkin became the first goalie to win seven straight home games in the postseason since Chicago's Corey Crawford in 2014. He allowed two goals or fewer for the seventh time in his past eight games.

Vasilevskiy gave up six goals on 34 shots after allowing three goals total in the four-game sweep of the Florida Panthers.

"This isn't on him at all," Tampa Bay coach Jon Cooper said of Vasilevskiy.

New York scored on its first shot when Kreider lifted a one-timer from the circle over Vasilevskiy's stick after getting a cross-ice pass from Zibanejad. Stamkos tied it a little over six minutes later when he blasted a slap shot from the right point after getting a drop pass from Jan Rutta.

Vatrano made it 2-1 at 7:50 of the second by putting a wrist shot from the middle of the slot past Vasilevskiy's stick. However, 42 seconds later, Palat backhanded the rebound of a Stamkos shot past Shesterkin.

--Larry Fleisher, Field Level Media