Schmidt gave the Panthers a 1-0 lead at 4:15 of the first period with a one-timer from above the right circle that beat Vasilevskiy to the far post. Sam Reinhart made the setup pass from the left point.
It was the third goal this series for Schmidt, who also had the game-winner in the 6-2 win in Game 1 on Tuesday.
After Hagel was assessed the major penalty for his hit on Barkov, Tampa Bay was able to successfully kill off all five minutes to keep it a one-goal game with 5:09 remaining.
"The refs make the call," Lightning coach Jon Cooper said. "Was I a little surprised that it was a five? But it was. They made that call, so we had to dig in and I think the boys did a great job of digging in there. Five minutes in a 1-0 game with 8-9 minutes to play. That's a tough situation to be in."
Bennett, however, scored an empty-net goal with four seconds left for the 2-0 final.
"It's exactly what we wanted to do, come in here and win the first two," Bennett said. "Obviously, the games aren't perfect. There were a couple mistakes by us tonight, but that will happen. Guys are helping each other out, bailing each other out, and 'Bobby' played unbelievable in net, bailed us out a bunch."
Jake Guentzel had an opportunity to score for Tampa Bay just 53 seconds into the game, but his shot toward an open net missed above the crossbar.
Lightning forward Brayden Point then had a point-blank opportunity at 1:52 of the first period, but he missed the open net high and wide left. Bobrovsky later stopped Point alone in the slot at 17:57 of the second period.
"We've got to get more pucks to the net and try to create some havoc that way and maybe break them down," Guentzel said. "You've got to get people in front of Bobrovsky."
Bobrovsky also made a glove save on a slap shot by J.J. Moser, who had an open look from the right circle at 16:33 of the third period.
"We had enough chances," Cooper said. "In a game this tight, some nights they go in, actually most nights they go in. Tonight they didn't, unfortunately. It's tough. There are two good teams ... good, tight teams. Teams check, that's what happens. It's the playoffs."
Said Bennett on Bobrovsky: "It's pretty incredible. Obviously, we've seen it for the last couple of years now. When the moment gets bigger, that's when he just seems to be more on his game. He made some incredible saves tonight. It's impressive to see."
The Panthers held the Lightning to just three shots on goal in the third period and were 5-for-5 on the penalty kill.
"We defended very well," Lundell said. "We didn't give too much to them. We were pretty aggressive and then we have Bob."
NOTES: Schmidt became the second defenseman in the NHL’s modern era (since 1943-44) to score the game-winner in each of his team’s first two games of the playoffs, joining Nicklas Lidstrom, who did it for the Detroit Red Wings in Games 1 and 2 of 2007 Conference Quarterfinals. … The Panthers became the first team to shut out the Lightning in a playoff game at Amalie Arena since the Capitals in Game 7 of the 2018 Eastern Conference Final. ... Lightning forward Nikita Kucherov has not scored in his past 12 playoff games and was minus-1 in 20:58 of ice time with eight shot attempts (one on goal). ... Lightning forward Anthony Cirelli, who was a game-time decision, had four hits and was 11-for-17 on face-offs in 15:09 of ice time. … Tampa Bay has lost seven of its past eight playoff games dating back to 2023.
