Anthony Cirelli and Jake Guentzel each had a goal and an assist for the Lightning (20-11-2), who scored twice short-handed and have won six of seven. Andrei Vasilevskiy made 42 saves.
"We won a game 6-2 tonight,” Tampa Bay coach Jon Cooper said. “If anyone was in the building it wasn't probably a 6-2 game. I think we caught a team that has been a little up and down lately. We were able to … get out of a first period where they controlled a lot of the play with the lead. That was fortuitous for us.
"We came out in the second period and did our thing -- got the lead and found a way through the game. The goalie was outstanding for us. We executed on special teams. Is that a recipe to make the playoffs and go far in the playoffs? No."
Vincent Trocheck had a goal and an assist for the Rangers (16-18-1), who have lost six of seven and 14 of 18. Igor Shesterkin allowed five goals on 13 shots before he was pulled at 8:08 of the second period, and Jonathan Quick made 11 saves in relief.
"Right now, it's just frustrating,” New York coach Peter Laviolette said. “We're in the business of winning hockey games and we're not getting it done right now, so it's tough to sit here and tell you good things. We're losing hockey games, we need to win hockey games and we're not getting that done.”
Kucherov gave Tampa Bay a 1-0 lead with a power-play goal at 2:27 of the first period, scoring on a chip-in from close range off a pass across the slot by Point.