TAMPA, Fla. -- The New York Rangers let another game slip away.
"This hurts," New York captain Jaromir Jagr said after the Rangers' season-high fifth consecutive loss.
"I don't know what to say. If somebody would have told me before the third period it's going to happen, I would say 'You're crazy.' But it happened."
The Lightning appeared headed to their ninth loss in 12 games, trailing 3-0 after two periods. Boyle changed the momentum with two goals in the first 2:29 of the third.
After assisting on Vincent Lecavalier's power-play goal that tied the score at 5:56, Boyle completed his first career hat trick on a wrist shot from the slot to make it 4-3 with 8:57 left.
"It's an awesome feeling," Boyle said.
New York got goals from Martin Straka, Blair Betts and Aaron Ward. The Rangers also blew a lead in their previous game, allowing three goals in the third period of a 3-2 loss at Florida on Thursday night.
Rangers coach Tom Renney said Saturday's loss was not the low point of the season.
"It sounds crazy to say that, but I think this is important stuff, I really do," Renney said. "I'm not going to dress up a pig's ear, it is what it is. But you know what? We will be better for this."
Boyle's first goal, 62 seconds into the third, came on the power play. It was a complete reversal from the first when Tampa Bay had three power plays during the opening 8 minutes, but had just three shots and failed to score.
"I don't think our top guys were ready to go, but they battled back," Tampa Bay coach John Tortorella said. "I think our top players put us in a hole, but our top players got us out of that hole. That's what it's about."
The Lightning have won six times in 17 games when trailing after the second period. The Rangers dropped to 12-2-2 when ahead after 40 minutes.
Straka put the Rangers up 1-0 on a rebound during a 5-on-3 power play at 16:37 of the first. Betts made it 2-0 with 51.8 seconds left in the period.
Ward extended the Rangers' advantage to 3-0 at 8:17 of the second on his first goal in 26 games.
"It's frustrating," Lundqvist said. "We have a 3-0 lead, and I think we should win this game."
"We got the momentum on our side and we got it going," Holmqvist said. "It's a great feeling when you get comeback like that."
- Boyle has eight goals this season. He hadn't scored a goal in his previous six games.
- Rangers RW Jed Ortmeyer scored the game-winning goal late in the third for Hartford of the AHL on Friday night. He was sent to the minors for conditioning earlier this month.
- Tampa Bay RW Martin St. Louis had his five-game goal-scoring streak end.
- Nylander had an assist.