TORONTO (AP) Coach Barry Trotz has spent the past two seasons attempting to instill a team-first, all-in identity with the New York Islanders.

No more was that evident than Saturday night, when the Islanders handily confronted their biggest test of the year - decades perhaps - in beating the Philadelphia Flyers 4-0 in Game 7 of the second round series.

The Islanders advanced to the Eastern Conference finals for the first time since 1993, where they'll face the Tampa Bay Lightning.

The win came courtesy of a backup goalie, Thomas Greiss, stopping 16 shots for his first playoff career shutout in his first Game 7. Brock Nelson scored a goal and set up two others. And defensemen Scott Mayfield, with his first career playoff goal, and late-season trade addition Andy Greene, spurred the victory by scoring 3:46 apart in the first period.

''We didn't get small by the moment. We got big by the moment,'' said Trotz, who landed in New York after leading the Washington Capitals to a Stanley Cup championship in 2018.

''I liked the fact that we recognized when we're at our best. And when we're at our best, there's always a sharp focus,'' he added. ''It's the commitment. If you need to block a shot, you block a shot. Don't go halfway in, be all in.''

It was a game in which the Islanders outshot the the Flyers 26-16, and showed resilience in bouncing back after losing the past two games in overtime.

For Nelson, the win helped ease the memories of past Islanders playoff losses, including the sting of losing Game 7 to Washington in the opening round of the 2015 playoffs.

''I'm sure everybody remembers that day. It wasn't our best game, and it's always tough losing a Game 7,'' Nelson said. ''And getting this one tonight definitely feels good.''

The Flyers ran out of gas, with coach Alain Vigneault pulling Carter Hart for an extra attacker with seven minutes remaining, which led to Anthony Beauvillier sealing the win with an empty netter.

Hart stopped 22 shots.

''After they scored that first goal, we just never had that same bounce or the same pop,'' Vigneault said. ''We weren't good enough tonight. That's why we lost.''

Flyers forward Sean Couturier returned after missing Game 6, and revealed he had a sprained knee ligament.

''We didn't create enough. we didn't win enough 1 on 1 battles to get our chances,'' said Couturier, who hit the post in the opening minute. ''It wasn't good enough.''

Defense became an issue for Philadelphia. After allowing just nine goals through the first seven playoff games, they closed giving up 31 in their last nine.

Philadelphia's power-power play unit particularly fizzled in closing the playoffs going 0 for 17 over its final eight games, and converting just 4 of 52 chances.

The Islanders became the third team of the second round of the playoffs to win Game 7 after squandering a 3-1 series lead. The Dallas Stars and Vegas Golden Knights advanced to the meet in the Western Conference finals after each won Game 7 of their series on Friday night.

Mayfield opened the scoring 9:27 into the game. The Islanders worked the puck around the top to Mayfield at the right point, from where he had plenty of room to skate in and snap a shot in off the far post, with Mathew Barzal causing havoc in front.

The goal provided Mayfield some payback after his broken stick led the Flyers rushing up the ice and Ivan Provorov scoring in double-overtime in Game 6.

''Just kind of down the past couple of days,'' Mayfield said. ''It's a confidence boost. Game-winner, Game 7 to go to the Eastern Conference finals, I don't think I'd be scoring it. But I had a lane, just happy I could put it away.''

A poor clearing attempt, picked off by Nelson, led to Greene's goal, set up Derick Brassard cross-ice feed into the left circle.

The rest was up to Greiss, making his third appearance of the series, and second start, in place of Semyon Varlamov, who allowed nine goals on 63 shots in losing the past two games in overtime, including a 5-4 double-overtime loss in Game 6.

''It was the best defensive game I've seen the team play,'' Greiss said. ''It's a great achievement for the whole team, for fans. I'm happy to help.''

The Islanders face a short turnaround in having to travel to Edmonton, Alberta, to face the well-rested Tampa Bay Lightning in a conference final series that opens Monday. The Lightning have been off since a 3-2 double-overtime win over Boston in Game 5 on Monday.

NOTES: The Flyers are 9-8 in Game 7 and 1-18 when trailing a playoff series 3-1. Their only series win came in rallying from a 3-0 deficit against Boston in the second round in 2010. ... The Isles improved their Game 7 record to 4-5, and 1-2 against Philadelphia, after losing to the Flyers in the semi-finals in 1975 and their last playoff meeting, a second-round series in 1987. ... The Islanders improved to 11-0 when leading a series 3-1.

UP NEXT

Islanders: Eastern Conference finals against Tampa Bay on Monday at 8 p.m. EDT.

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