Palat made it 2-0 at 14:57 when he scored on a rebound after Point got around defenseman MacKenzie Weegar and his shot went off the crossbar.
"It was a good feeling," Tampa Bay defenseman Ryan McDonagh said. "You want to play with the lead. It allows us to just play high percentage and you don't have to force things or chase the game. I thought we did a good job continuing to create things. Even when you have the lead there, you don't want to just sit back completely and give up a lot of ice. Our group feels confident in those situations."
Marchment made it to 2-1 at 14:21 of the second period when he redirected Carter Verhaeghe's pass in front of the net for his first NHL playoff goal.
Tampa Bay, which was 3-for-4 on the power play in Game 1, killed off two penalties in the third period and was 3-for-3 for the game.
"Our power play was instrumental in Game 1, and the PK was instrumental in Game 2," Cooper said. "Usually you don't have a ton of power plays, but they get three tonight. It always seems to work that way; you have the lead and you get something called on you late and we had to kill it off. I thought that was a huge part of the game that we killed it off. Guys were laying out blocking shots, getting clears. You need to do that to win hockey games this time of the year and guys pulled through."
Gourde scored into an empty net with 1:25 remaining for the 3-1 final.
"We moved better in the offensive zone [in Game 1] and we created chances in the offensive zone more than we did today," Panthers captain Aleksander Barkov said. "But sometimes it's gonna be like this and we just have to find a way. It doesn't matter how you win, you've just got to win."
NOTES: Each team used seven defensemen, with Luke Schenn entering the lineup for Tampa Bay and replacing forward Mathieu Joseph, and Stralman replacing Bennett for Florida. … Palat's goal was his 33rd in the playoffs, tying Martin St. Louis for second place in Lightning history behind Nikita Kucherov (38). … Driedger became the first goalie to make his NHL playoff debut on his birthday. … Marchment's goal came 10 days shy of the 19-year anniversary of his father's first NHL playoff goal, and each came against the defending Stanley Cup champions; Bryan Marchment scored for the Chicago Blackhawks against the Pittsburgh Penguins on May 28, 1992.