The 21 year-old also scored a game-winner in double overtime at Montreal in the second round. Ondrej Palat added two goals and an assist, while Tyler Johnson recorded his NHL-leading 12th goal in this year's playoffs, along with an assist. Steven Stamkos and Alex Killorn each had a goal and an assist for the Lightning, who came back from a 2-0 deficit, and then blew a two-goal lead.
Henrik Lundqvist had just made a game-saving stop on J.T. Brown's breakaway, before Kucherov ended the game for good at Amalie Arena.
The Rangers forced overtime when Dan Boyle slammed home a rebound with 1:56 left in regulation. Jesper Fast had two goals in the loss, while Derick Brassard and Ryan McDonagh added power-play goals of their own. New York came back from a 4-2 deficit when Fast scored late in the second period, and then McDonagh tied it early in the third.
Stamkos netted his fifth goal of the playoffs, following 43 during the regular season, to get the scoring going for Tampa Bay.
Ben Bishop made 23 saves for the Lightning, while Lundqvist recorded 34 saves, giving up six goals for the second straight game.
Game 4 of the series will take place tomorrow night in Tampa Bay.