Kucherov delivered his second winner of the playoffs 3:33 into the extra period Wednesday night, giving his team a 6-5 victory and 2-1 lead in the best-of-7 series that continues Friday night at Amalie Arena.
The 21-year-old Russian, part of the high-scoring Triplets line that is leading Tampa Bay's playoff run, also gave the Lightning a win in double overtime at Montreal in the second round.
Linemate Ondrej Palat had two goals and an assist, and Tyler Johnson — the other triplet — had his playoff-leading 12th goal, as well as an assist.
"They've impressed me for a long time, and now they're impressing the world," Lightning coach Jon Cooper said. "It's fun to watch."
Steven Stamkos and Alex Killorn each had one goal and an assist for Tampa Bay. The Lightning overcame an early 2-0 deficit and won despite also squandering a two-goal lead to the resilient Rangers.
The winner came about a minute after New York goalie Henrik Lundqvist made a terrific stop on J.T. Brown's breakaway.
"In overtime, everybody's thinking everybody be a scorer," Rangers coach Alain Vigneault said. "Hank had stopped a breakaway right before that, and sometimes things happen."
New York tied it at 5 on Dan Boyle's rebound with 1:56 left in regulation. Jesper Fast scored twice, and the Rangers also got power-play goals from Derick Brassard and Ryan McDonagh.
"It was deflating, but at the same time ... we felt like we deserved the game," Johnson said about losing the lead late in regulation.
"We worked hard and were happy with the way we played," added Johnson, whose hat trick keyed the Lightning's 6-2 road victory in Game 2. "Obviously didn't want to give up as many goals, but things happen. They're a great team. We knew if we just kept on playing, played our game, we were going to get a bounce. Luckily for us, we got that bounce before them."
The Rangers came back after trailing 4-2, with Fast scoring his second goal late in the second period and McDonagh converting a power-play opportunity early in the third.
"We've got a pretty quick team and they have a quick team," Cooper said. " I don't know how it looks to everybody else and I don't know how it looks on TV, but when you're standing there, it's just, pardon the pun, it's lightning fast. It's just amazing how the skill level and the speed and how these guys can play the way they do at that high pace."
After splitting the first two games in New York, the Rangers talked about cleaning up mistakes that cost them in Game 2, as well as the need to create more scoring opportunities against Lightning goalie Ben Bishop.
They didn't have a lot of chances early, but did make the most of team.
Brassard scored on the first shot of the game, sending the puck over Bishop's shoulder from the left circle. Fast made it 2-0 with the nifty backhand made possible, in part, by a big hit on Tampa Bay's Matthew Carle. With the Lightning defenceman slow to get to his feet, Fast skated freely up the middle before taking a pass from Chris Kreider and barrelling in alone on Bishop to score his second goal of the playoffs and give the Rangers the type of start they felt they needed to reassert themselves.
But Tampa Bay would not be denied.
Stamkos got the Lightning going with his fifth goal of the playoffs. Lundqvist cleared a bouncing puck with his stick directly to the high-scoring Stamkos, who had 43 goals during the regular season and is a two-time Maurice Richard Trophy winner. Johnson assisted on Palat's goal to make it 2-2, and the linemate returned the favour with a perfect pass through the middle to Johnson, camped to Lundqvist's right for an easy tap in that put the Lightning up 3-2.
Killorn increased the lead to 4-2 for all of 29 seconds. Fast's second goal of the night trimmed New York's deficit to one goal at 17:47, setting the stage for an entertaining third period.
McDonagh's power-play goal made it 4-4 less than 3 minutes into the period. Palat's second goal of the night put the Lightning back in front until New York pulled even again on Boyle's late goal.
Bishop finished with 23 saves for Tampa Bay. Lundqvist stopped 34 of 40 shots, giving up six goals for the second straight game.
"I just need to be more consistent," Lundqvist said. "Challenge the shooter."
Notes: Derek Stepan's assist on New York's first goal gave him a playoff career-best, six-game points streak. ... The Lightning went 1 for 2 on the power play, with the Rangers becoming the last team to allow a power-play goal on the road this post-season. ... Johnson tied Tampa Bay's record for most playoff goals in one year. Brad Richards and Ruslan Fedotenko both scored 12 during the Lightning's run to their only Stanley Cup title in 2004. ... Rangers RW Mats Zuccarello, who hasn't played since taking a shot off the helmet in Game 5 of New York's first-round series against Pittsburgh, skated after team practice for the second time this week. There's still no timetable for his return.Suggest a correction