Point completed the hat trick at 14:48 to extend the lead to 5-3, and Kucherov added an empty-net goal at 16:22 for the 6-3 final.
"Our line was minus-2 to start the game," Point said. "These are huge points and we're battling for a playoff spot. We definitely took it personally and didn't want to let the team down."
Artemi Panarin gave New York a 1-0 lead at 13:58 of the first period. He scored with a one-timer from the bottom of the left circle off a pass from Vincent Trocheck, who toe-dragged Darren Raddysh in the slot on a 2-on-1.
Braden Schneider made it 2-0 at 16:56 with a one-timer from the left hash marks off a pass from Mika Zibanejad from below the goal line.
"The first 30 minutes we came out with a lot of energy," Trocheck said. "Anytime you play against good teams there's going to be swings. We had a few defensive lapses. Things were back and forth, but we gave up a few too many opportunities in our D-zone."
Point cut it to 2-1 at 12:41 of the second period. He finished a return pass from Kucherov after forcing a turnover by Rangers forward Jonny Brodzinski in the neutral zone.
Anthony Duclair tied it 2-2 at 18:43 when he buried a rebound into an open net from the right circle.
"I hope this gives us some belief down the stretch here that we're not out of any game," Point said. "We can climb back and we played the right way to climb back. When we play like that we get results."
Roslovic gave New York a 3-2 lead at 1:48 of the third period, scoring with a one-timer from the left circle off a cross-ice pass from Adam Fox.
It was Roslovic's first goal in four games with New York since being acquired in a trade with the Columbus Blue Jackets on March 8.
"He's been awesome. Great kid, great player," Rangers forward Chris Kreider said. "He's trying to get better every game on the line. He's pretty bummed that we lost the game, though. I think everyone in the room is."
NOTES: Doug Crossman (Nov. 7, 1992) and Kucherov (Nov. 24, 2023) are the other players in Lightning history with a six-point game. ... Kucherov has 18 points (three goals, 15 assists) during a nine-game point streak. ... Kreider had an assist and has five points (two goals, three assists) during a five-game point streak. ... Schneider's goal was his first since Dec. 27 (33 games). ... Defenseman Victor Hedman was plus-4 and had two assists in his 1,038th NHL game, which passed Vincent Lecavalier for second in Lightning history. ... Duclair eight points (five goals, three assists) during a four-game point streak.