(AP) -- Whenever the New York Islanders got behind, they fought their way out of trouble.

And when they finally got the lead, they didn't give it back.

John Tavares had a goal and two assists, including one that set up Kyle Okposo's go-ahead goal early in the third period, and the Islanders beat the Florida Panthers 5-4 in Game 1 of the teams' Eastern Conference quarterfinal series on Thursday night.

Thomas Greiss survived a shaky beginning and made 42 saves for the Islanders in his first playoff start, and Brock Nelson, Frans Nielsen and Ryan Strome added goals for New York.

Home-ice advantage in the series now belongs to the Islanders, and they can take a 2-0 lead back to Barclays Center if they prevail when the series resumes in a quick turnaround on Friday night.

Reilly Smith had two goals, Jussi Jokinen had a goal and two assists and Teddy Purcell also scored for the Panthers. Roberto Luongo stopped 21 of 26 shots.

Florida took the lead on three occasions in the first two periods, and the Islanders came back and tied it every time.

The Panthers -- somewhat predictably, since the franchise hadn't played a postseason game in four years -- came out flying, getting on the board just 1:55 into the game when Purcell tapped a perfect pass from Jiri Hudler into a wide-open net to start the scoring.

Later in the first, Jokinen deflected Brian Campbell's shot from the high slot for Florida's second goal, and Smith got his first of the night 1:31 into the second period.

And after each one, the Islanders seemed most unfazed.

Nelson and Nielsen had tying goals in the first period and Tavares sent the teams into the second intermission tied at 3-3 when he took a pass from Okposo and scored his sixth career postseason goal.

Tavares and Okposo worked their magic again early in the third, Tavares poking the puck from Florida defenseman Campbell to set up Okposo and put New York on top to stay. Strome made it 5-3, before Smith got Florida back within one less than a minute later -- slamming his gloved hands into the glass in celebration.

Greiss made sure that was the last moment Florida enjoyed, stopping 15 of the shots he faced in the final period.

NOTES: Florida was 27-0-2 when scoring at least four times in the regular season, and 36-6-6 when scoring first. ... The Islanders also had leads of 1-0 and 2-1 in last year's first-round series with Washington, before bowing in seven games. ... Florida fell to 4-4 all-time in Game 1s. The Panthers have never won a series after dropping the opening game, though this is only the eighth series in franchise history. ... Florida's Jaromir Jagr played in his 203rd postseason game. The Panthers were playing in their 39th. ... The Islanders have won 30 of the 38 games all-time in which Tavares has a three-point night. ... The game wasn't a sellout, drawing 17,422 -- about 2,000 less than capacity.