Nikita Kucherov had three assists to run his point streak to nine games (four goals, 14 assists), including five straight multi-point games. Nick Paul and Jake Guentzel scored, and Jonas Johansson made 12 saves for the Lightning, who outshot the Rangers 35-13.
"We did it to ourselves," Rangers captain J.T. Miller said. "There was no urgency today. We dipped our toe into the game and got outplayed basically the whole time. It's unacceptable. We're trying to develop a standard and an identity around here and that was certainly not it."
Miller scored, and Igor Shesterkin made 31 saves after making 19 in a 6-2 win at the Boston Bruins on Friday. The Rangers (13-12-2) had a three-game winning streak end. Their 13 shots on goal were a season low.
"We got outcompeted from the drop of the puck," Rangers coach Mike Sullivan said. "There's got to be a willingness and a want to be first to pucks, to embrace physicality. We knew the type of game it was going to be. That team, they've got hard skill, they compete and they skate. That was the type of game it was going to be. I don't think we had the wherewithal to match the intensity. I just feel we lost puck battles all over the rink and it's hard to establish any sort of game that you want to play if you don't win puck battles."
Hagel gave the Lightning a 1-0 lead at 10:53 of the first period. His shot from the top of the left face-off circle went in off Rangers defenseman Carson Soucy's right skate.
Tampa Bay was outshooting the Rangers 10-1 at that point. It had a 19-2 edge in total shot attempts.
"Sometimes in games, that'll be happening where you'll be putting all the pressure on and then one goes in the back of your net," Hagel said. "Glad it went in on our side and obviously we were able to build off of it, continuing throughout the game, continuing to play the exact same way."
Hagel made it 2-0 at 8:57 of the second period. He took a stretch pass from Kucherov in for a breakaway on Shesterkin, who did the splits and stopped Hagel's initial shot with his left pad. But Hagel recovered the puck in the slot and lifted it over Shesterkin's pad.
"Gladly the 'D-man' went to the left side so I had the time to pull it out and put it up," Hagel said.