TAMPA, Fla. -- After a 2-6-2 start, the New York Rangers have now won three of four games and J.T. Miller's overtime goal might have sparked their biggest win of the early season.

Miller scored 1:19 into overtime, lifting the Rangers to a 2-1 victory over the Tampa Bay Lightning on Thursday.

"They're probably the best team in the league last night, and after our game against Vegas, we felt it was a step in the right direction," New York defenseman Marc Staal said after holding the league's top scoring team to a single goal. "We wanted to make sure we backed it up with a win, and we did it against a very good team."

Miller beat two players as he swept in front of the net and then fired a top-shelf shot to beat Andrei Vasilevskiy, who had made 33 saves to keep the Lightning in a game in which they were outplayed.

"He made a lot of big saves for us, but they're a fast team and they got a jump on us a few times to create some chances," Lightning center Brayden Point said.

New York (5-7-2) picked up its first road win of the season after starting the year 0-3 away from home, while the Lightning (10-2-2) have stumbled twice after opening the season with six straight home wins.

"To be able to put it together for a good little stretch feels good," Miller said of his third goal of the season, seconds after intercepting a wraparound attempt by Nikita Kucherov. "Especially on the road, first away win of the year. We're going to enjoy tonight and get ready for another good test for us."

The Lightning were able to overcome a slew of turnovers in their own zone, with Vasilevskiy making more than his share of saves on breakaways from errant passes.

New York goalie Henrik Lundqvist stopped 27 shots.

The Lightning have the league's top two scorers in Kucherov and Steven Stamkos, and New York held both without a point, limiting the Lightning to four shots in the third period.

The defensive stalemate was a surprising change of pace after the Lightning won an 8-5 game at Florida on Tuesday and the Rangers won 6-4 against Vegas.

Tampa Bay appeared to take a 2-1 lead early in the third, but Alex Killorn's goal was wiped out on goalie interference. The Lightning challenged the call, but a review confirmed that Gabriel Dumont was in the crease. Cooper strongly disagreed with the call after the game, but said his team was fortunate to get to overtime.

"He clearly got us the point for us tonight," Lightning coach Jon Cooper said. "He's been doing that all year for us. He's been our MVP. It's one of 82. We got a point out of it, so we're not walking away empty-handed.

"It's one more point than we had a few hours ago, so let's turn the page and move on."

The Lightning tied the game in the second period on just their second short-handed goal of the season. Yanni Gourde converted a two-on-one on a pass from defenseman Victor Hedman to beat Lundqvist on the stick side at 11:00. The goal was Gourde's third of the season and the first short-handed goal allowed by the Rangers this season.

New York led 1-0 after the first period, scoring on a three-on-one break during four-on-four play at 18:34. Chris Kreider scored his fourth goal of the season on passes from Mika Zibanejad and Brady Skjei.

Tampa Bay started slowly, managing only two shots on goal in the first 10 minutes. The Rangers outshot the Lightning 13-8 in the opening period, but led just 1-0 thanks to strong play by Vasilevskiy, who stopped Miller on an odd-man rush and Kevin Shattenkirk on a breakaway.

NOTES: Lightning C Cedric Paquette missed a seventh consecutive game with an upper-body injury, while D Slater Koekkoek and D Andrej Sustr were healthy scratches. ... The Rangers had D Brendan Smith and C Paul Carey as healthy scratches. ... Tampa Bay stays home to play Columbus on Saturday before a three-game trip to California next week, while New York plays at Florida on Saturday before returning home for its next three games.