TAMPA, Fla. -- Turns out the New York Rangers haven't cornered the market on having "no quit" in the Stanley Cup playoffs.

The Tampa Bay Lightning rallied from a 2-0 deficit in the second period to win Game 3 at home on Sunday night 3-2, cutting the Rangers' Eastern Conference finals lead to 2-1. Winger Ondrej Palat scored the game-winning goal with 42 seconds left in regulation on a perfect pass from Nikita Kucherov, who factored in on all three Lightning goals.

"It wasn't an ideal situation, but there's no quit in our group. We were down 2-0 in the series. It was pretty much all on the line in the third," said captain Steven Stamkos, whose power-play goal 1:22 into the third tied the score at 2-2.

Stamkos ticked off what worked for the Lightning in Game 3 that hadn't worked in the first two games in New York: the 5-on-5 game being in their favor; pumping 51 shots and 83 shot attempts on goalie Igor Shesterkin while getting a strong 28-save effort from Andrei Vasilevskiy; a penalty kill that allowed two Rangers power-play goals but came up big during a four-minute high-sticking penalty on Kucherov in the third period; and, finally, getting a clutch goal from Palat when they needed it.

"We've seen this for years from Palat. The quiet kid, doesn't say anything. All he does is give you everything he has, every shift. He's got that ability to play that blue-collar game with white-collar players, and that's a great trait to have," Lightning coach Jon Cooper said. "He's usually the third guy talked about on the lines he plays on. But he comes through."

The Rangers, whose marketing slogan on social media this postseason has been #NoQuitInNY, had an opportunity to potentially put the series on ice with a Game 3 win. Heading into Sunday, teams that take a 3-0 lead in a best-of-seven series hold an all-time series record of 198-4 (.980). Teams that take a 3-0 lead in a best-of-seven when starting at home hold an all-time series record of 144-3 (.980).

"It's not easy. You get on the bench and you're down 2-0 in the game and 2-0 in the series. You feel the momentum going the other way," Stamkos said. "But that's what it is to find a way this time of the year. We've done it for a couple of years now, and tonight was another example of finding a way to just win one game. That's what we talked about before the game: Will your way to a win tonight and whatever happens, happens. Just another gutsy effort tonight."

Game 3 was scoreless after the first period, leading into a wild second period.

The teams were playing 4-on-4 when Mika Zibanejad took an interference penalty. The Lightning had 1:32 of 4-on-3 power play time -- with Shesterkin making two saves and Rangers forward Barclay Goodrow clanging one off the post short-handed. But winger Corey Perry was whistled for slashing the mask of Shesterkin, who wildly tossed his stick to the end boards. Perry was furious entering the penalty box.

The teams then played 3-on-3 for 13 seconds and then 4-on-4 for 15 seconds as additional players left the penalty box. The Rangers eventually went on the power play and 30 seconds later Zibanejad blasted a shot through Vasilevskiy for the 1-0 lead at 7:37 of the second period.

The Lightning took another penalty against Shesterkin at 8:23 of the second period, as forward Riley Nash -- playing in his first game since March 20 -- bumped him on a Tampa scoring attempt. Again, the Rangers made the Lightning pay: Chris Kreider put in the rebound of a Zibanejad shot to make it 2-0 at 9:44 of the second.

It was the 10th postseason goal for both Zibanejad and Kreider.

The Lightning crowded Shesterkin's crease during Game 3, which Rangers coach Gerard Gallant didn't like. "It fazes me more than him. I don't like it," he said. "I don't think it's a big part of it. Hopefully, when we talk to the (officiating) supervisor tomorrow, they'll take care of some of that because it wasn't right," he said.

Cooper pushed back.

"I don't think they could have called it any tighter. What was there, three penalties on goalie interference?" he asked, as Rangers forward Frank Vatrano joined Perry and Nash in getting whistled for it. "Is part of this game being net-front? Yes. Is that in our game plan to knock people over? No. The first one, we're on a 4-on-3 power play. We took ourselves off it. Trust me, we're not trying to hit the goalie. I think we were more angry about it than the Rangers were at that point."

Tampa Bay got one back on a power play of their own, as defenseman Jacob Trouba went to the box for interference. Kucherov scored on a blast to Shesterkin's left at 10:50, scoring his second of the series and sixth of the playoffs.

After the second period ended 2-2, the Lightning tied the game on -- what else? -- a power-play goal, as Trouba made his second straight trip to the penalty box, this time for holding. Perry made a cross-ice pass to Stamkos for a one-timer at 1:22 for his sixth of the playoffs.

The Lightning killed off a four-minute power play after the Kucherov high stick. Then it was Palat to end it with the game's first even-strength goal, scoring his 10th game-winning playoff goal, passing former teammate Tyler Johnson for most in franchise history.

In the process, Palat got his team back into the series ahead of Tuesday night's Game 4.

"You either fold up or you go out there and do it," Stamkos said. "Did we expect to score with 40 seconds left? No. We were excited to tie it up and thought it was going to overtime. That can be a big momentum swing for our group."