NEW YORK -- John Tavares tied it in the final minute of regulation and scored the winner at 10:41 of the second overtime, leading the New York Islanders past the Florida Panthers 2-1 Sunday night and into the second round of the playoffs for the first time since 1993.

Tavares skated in and fired an initial shot that Roberto Luongo saved, but the New York captain got the rebound, wrapped around the net and stuffed the puck in to end the longest home game in Islanders history.

"I don't think we tried to put too much pressure on ourselves knowing we weren't here for all of that," Tavares said of New York's playoff series drought. "But certainly a lot us have been here for a while and it was time for us."

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The Islanders will next face Tampa Bay.

Thomas Greiss finished with 41 saves in the teams' second straight two-overtime game and third in the series to go past regulation. The Islanders won Game 3 here 4-3 in the first extra period, and took Game 5 in Florida 2-1 at 16 minutes of the second OT.

#ISLES WIIINN!!! Round 1 victory ✅

Round 2 HERE WE COME!!! YES! YES! YES! #DriveFor5 pic.twitter.com/H4ta3mBeVH

— New York Islanders (@NYIslanders) April 25, 2016

And, in Game 6, Tavares sent the Barclays Center crowd into a frenzy with his series winner, and was quickly mobbed by his exhausted but ecstatic teammates.

"When I got the rebound, I realized how far he came out," Tavares said. "I had a good step and just tried to, not take my time, but really make sure I had control of the puck. And obviously once you get around the net, make sure it goes in."

Jonathan Huberdeau scored late in the first period for Florida, and Luongo stopped 49 shots for the Panthers.

On the tying goal with just under 54 seconds left in the third period, Islanders defenseman Nick Leddy took the puck behind his own empty net, skated all the way down the right side and sent a centering pass from behind the Panthers' goal. Nikolay Kulemin tried to tip it in, but Roberto Luongo dived to his left on top of it. But the puck trickled out from underneath him to his right, and Tavares swooped in and put it in for his fourth of the series.

"I just tried to get lost in coverage and just hope the puck kind of came to me," Tavares said. "Lucky enough, it just squirted under Luongo and it doesn't get any easier than that."

Congrats, @NYIslanders! We're honoring their series victory over the Panthers w/ blue and orange. #Isles pic.twitter.com/UBtlFaeAiz

— Empire State Bldg (@EmpireStateBldg) April 25, 2016

Both teams had solid chances in the extra periods, but were stonewalled by the goalies.

Reilly Smith, held without a point since having four goals and four assists in the first three games, fired a shot that deflected off the crossbar early in the second OT.

On an Islanders rush, Kyle Okposo got the puck on the left side, but his wrist shot was turned aside by Luongo near the 6-minute mark. Okposo was also open at the left side of the net, but Tavares' pass went between his skates.

Greiss smothered a wrist shot by Huberdeau with about 6 minutes remaining in the first OT.

"He played great," New York coach Jack Capuano said of his goalie. "You need goaltending and he came up big for us."

🚨🚨🚨🚨!!!!! TAVARES!!! YES!!!!

— New York Islanders (@NYIslanders) April 25, 2016

The Islanders pressed from the start of the third. Luongo stopped a pair of snap shots by Cal Clutterbuck and a slap shot by Leddy in the first few minutes of the period. Clutterbuck also had a backhand attempt denied by the goalie about 5 minutes in. Okposo had a couple of chances less than 2 minutes later, and Luongo stopped Travis Hamonic's snap shot after that.

With Huberdeau off for cross-checking, Tavares had a slap shot with about 6 1/2 minutes left, and Brock Nelson had a pair of chances seconds later.

The Islanders controlled the play for most of the opening period, but the Panthers took the lead just before the closing minute of the period after New York turned it over in its own zone.

Vincent Trochek sent a pass to Huberdeau, who spun and fired a shot from the high slot while falling down with the puck going over Greiss' blocker with 1:02 remaining. It was Huberdeau's first goal of the series and marked the fifth time Florida scored first.

Clutterbuck was bleeding after getting hit in the face with the puck about 6 minutes into the game and left the game to be treated. He returned for the start of the second.

NOTES: The Panthers were without C Nick Bjugstad, who lost his footing after being hit by an Islanders player and went face-first into the boards during the first extra period Friday night. Bjugstad did not travel with the team to New York and Florida coach Gerard Gallant said he was day to day. ... Jagr, who has not scored a goal in his last 37 playoff games, played in his 208th postseason game, tying Wayne Gretzky for 16th place on the all-time list. ...The Islanders improved to 7-0 with a potential clinching Game 6 at home, last accomplishing the feat against Washington in the first round in 1993.