Point’s six points were an NHL career high and tied for the most in Lightning history.
Kucherov had a goal and four assists for the Lightning (35-25-6), who hadn’t played since a 7-0 win against the Philadelphia Flyers on Saturday. Andrei Vasilevskiy made 25 saves.
Jack Roslovic had a goal and an assist for the Rangers (43-19-4), who had won three straight. Igor Shesterkin made 22 saves.
Point tied it 3-3 at 3:41 of the third period. He tried to make a move around Erik Gustafsson, who poked the point into his own net during a 4-on-4.
Steven Stamkos put the Lightning in front 4-3 at 12:45, scoring a power-play goal off a backhand pass from Point.
Point then 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.
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 five-hole from the left hash marks off a pass from Mika Zibanejad from below the goal line.
Point cut it to 2-1 at 12:41 of the second period when 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.
Roslovic responded to give 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.
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