Panarin cut it to 3-1 with a power-play goal at 16:27. After New York pulled Shesterkin to make it a 6-on-4 advantage, Panarin collected a loose puck in the right circle and beat Vasilevskiy high to the short side.
"It's not easy, but we can't be sad," Panarin said. "For sure it's not going to help us. Try to be positive. We have to be positive. We've been in a worse spot before, so we're OK. I hope we do well in [Madison Square] Garden. Our fans, nice to see again. Try to do something more."
Palat's empty-net goal made it 4-1 with nine seconds remaining.
Rangers forward Filip Chytil left the game in the second period with an upper-body injury after colliding with Lightning defenseman Victor Hedman along the boards. New York was also without forward Ryan Strome, who took the warmup but did not play because of a lower-body injury sustained in Game 3. Gallant said Chytil should be fine and that Strome is day to day.
"Every team is dealing with injuries," Rangers defenseman Jacob Trouba said. "We like the depth of our team. We think we can manage and overcome injuries. It's not something we're looking at or thinking about too hard. Do we miss them? Yeah. Do we hope they come back? Yeah. But you've got to be able to play without them."
NOTES: Tampa Bay is 11-1 in Stanley Cup Playoff history when Stamkos and Kucherov score. … Palat's goal the 16th of his career in this playoff round, the most among active players. … The Lightning tied their longest postseason home winning streak. They won six straight last season, from Game 2 of the Stanley Cup Semifinals against the New York Islanders through Game 5 of the Stanley Cup Final against the Montreal Canadiens. … Rangers defenseman Adam Fox had an eight-game point streak end. He was minus-3 in 26:34 of ice time. … Panarin has eight points (three goals, five assists) in the past seven games.