Only the final lead was safe in Game 4.
Tavares slammed in his own rebound in front after Brad Boyes fed him following a turnover by Penguins star Evgeni Malkin. It was the Islanders' third one-goal advantage in the game and the one that earned them a 2-2 tie in the highly entertaining series that has featured 5-4 and 6-4 finishes at Nassau Coliseum.
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Tavares was serenaded with cheers of "M-V-P" from the frantic crowd that is believing an upset is possible. Casey Cizikas shoved in a shot with 1:16 left to add some much-needed insurance.
"We found a way today. Another roller coaster ride," Tavares said. "We learned from those games when we gave up leads -- a lot of us said that one bounce can change a season.
"Not sure what it was but we have had contributions offensively and defensively from everyone in our lineup. That makes us better."
Captain Mark Streit scored twice, and Brian Strait and Kyle Okposo also had goals. Evgeni Nabokov made 27 saves for the eighth-seeded Islanders, who know they will last at least six games with the top-seeded Penguins.
"You get into the playoffs, you put in so much effort to get here, we want to make the most of it," Tavares said. "We believe in this room. We have a lot of character. That's what we need."
Game 5 is Thursday in Pittsburgh.
James Neal, in his return after injuring his ankle in the series opener, scored in the first period. Malkin added a tying goal in the second, and Brandon Sutter and Pascal Dupuis provided the Penguins with a pair of one-goal leads they couldn't protect.
"Momentum shifts so quickly," Neal said. "Once you regain it you've got to keep it. You saw how energetic their crowd was and how much they fed off that. We just need to put this one behind us and get back to our game. I don't think we've gotten there yet."
Marc-Andre Fleury stopped only 18 shots during a difficult night. Penguins coach Dan Bylsma was noncommittal as to whether Fleury would be back in the net for Game 5. Veteran netminder Tomas Vokoun is ready and waiting should a change be made.
"He has had success and won hockey games against this team and has been successful this year," Bylsma said of Vokoun. "We're going to regroup and come back and come out for Game 5 with a new focus."
Pittsburgh beat New York 5-4 in overtime on Sunday in a game in which both teams squandered two-goal leads.
Dupuis gave the Penguins their second lead of the night just 41 seconds into the third period when he tipped in a shot from Chris Kunitz. It was Dupuis' fourth goal of the series.
The Islanders responded again, just as Pittsburgh did in erasing a pair of one-goal deficits. Streit netted the tying goal when his shot from the center of the blue line hit the skate of Penguins defenseman Douglas Murray and found its way in.
A second-period goal originally credited to Streit was changed to Tavares, then back to Streit.
The game continued its back-and-forth trend in the second period with each team giving up a one-goal lead, leading to a 3-3 tie heading into the third.
Streit put New York back in front from the left point with a long-awaited power-play goal. The Islanders had scored only one man-advantage goal in 11 chances over the first three games, and then failed on their first three opportunities in this one before connecting.
But as in the first period, the Islanders didn't enjoy the lead for long. Just 58 seconds later, Malkin raced into the New York end on a 2-on-1 rush and snapped a shot in from the right circle for his second of the series.
Pittsburgh then grabbed its first lead of the night on Sutter's first career playoff point. The son of Brent Sutter, a two-time Stanley Cup champion with the Islanders, snapped a shot from the left circle that beat a screened Nabokov over the left shoulder.
However, the young, pesky Islanders weren't deterred, and they got even with 1:24 remaining in the middle period.
Okposo continued his superb series by scoring for the third straight game, with some help from Fleury. Okposo sent the puck from behind the Penguins' net toward the front near the right post. Fleury was there, facing in Okposo's direction, when the puck hit him while he was crouched and found its way in.
Strait broke the Game 4 deadlock with 5:55 left in the first, just moments after his shot deflected high near the throat area of Sidney Crosby. The Penguins captain skated slowly, hunched over following a whistle, but he was back on the ice for his next shift.
The fans had been chanting "Princess Crosby" just before he was struck, and quickly cheered his injury. Crosby missed a big chunk of this season with a broken jaw.
Strait's goal was quite momentous as it was his first in the NHL -- regular season or playoffs. Strait, claimed off waivers by the Islanders from Pittsburgh in January, had never had a point in his previous six playoff games, and only five assists in 31 regular-season contests.
But Neal took a crisp feed from Malkin from the high slot to the right circle and beat Nabokov with a tough-angle shot inside the right post to tie it 45 seconds after Strait's goal.
- Strait's first point with the Islanders was against Pittsburgh on Feb. 5. He missed 27 games after breaking his left ankle on Feb. 18 and returned to the lineup on April 20 and played the final four regular-season games.
- Islanders D Andrew MacDonald sustained an upper body injury in the second period and didn't return.
- Sutter scored the winning goal for the Penguins in both of their visits to Nassau Coliseum in the regular season.
- Penguins D Brooks Orpik returned after missing five games with an injury.