UNIONDALE, N.Y. -- John Tavares said he needed to be better. On Saturday, he was, and it helped save the New York Islanders' season.
Tavares scored in the first period and played a huge role in Nikolay Kulemin's go-ahead goal in the third, giving the Islanders a 3-1 win against the Washington Capitals in Game 6 of the Eastern Conference First Round in what could be the final game played at Nassau Coliseum.
The best-of-7 series is tied 3-3 with Game 7 at Verizon Center on Monday (7:30 p.m. ET; NBCSN, SN, TVA Sports 2, MSG+, CSN-DC).
"It's just nice to capitalize on your chances," said Tavares, who had one goal through the first five games. "I think I had some good chances last game and it's just nice to capitalize, especially early.
"You just want to leave it out there. If I'm playing well, playing the right way both ways, I believe I'm going to create some opportunities. I just want to take advantage of those and I thought [Ryan Strome] and [Brock Nelson] were great today. I thought we did some good things. Now we need another one."
Jaroslav Halak made 38 saves for the Islanders, who are 26-18 when facing elimination; they are 16-5 at the Coliseum. Cal Clutterbuck scored an empty-net goal with 52.6 seconds left.
It was a particularly impressive win for New York, considering it played without injured defensemen Travis Hamonic, Lubomir Visnovsky and Calvin de Haan. Nick Leddy had two assists in 28:59 and Johnny Boychuk played 27:00.
"Basically it was the season on the line for us," Halak said. "They came out hard and played well. We need the same Monday night. It's going to be hard, but we all know why we're here."
John Carlson scored for the Capitals, who are 0-4 in Game 6 when holding a 3-2 lead in a best-of-7 series since 2006. Braden Holtby made 35 saves.
Washington is 3-9 in Game 7, 2-7 at home.
"They had some quality chances," Capitals coach Barry Trotz said. "Braden was pretty good. I thought that when we had some quality chances, Halak was pretty good. You had two pretty good goaltenders. It was just the desperation level of the Islanders that was just a little bit higher than ours. Now we are both desperate. It's a winner-take-all situation."
Kulemin, who had four goals since Jan. 19, broke a 1-1 tie with 9:27 remaining. Moments after Tavares was driven hard into the boards by Alex Ovechkin, Nick Leddy passed to Kulemin, who collected the puck in front and quickly beat Holtby with a forehand for his first Stanley Cup Playoff goal in his 13th game.
"I just tried to get to the net and I got hit there," Tavares said. "The puck kind of popped out."
Ovechkin said, "We had a good chance in the third, didn't score. It happens. They bounced back and Kulemin scored."
Tavares gave the Islanders a 1-0 lead 6:57 into game. After taking a pass from Strome, Tavares skated into the slot and eluded Carlson before putting a wrist shot past Holtby, who was screened by Nelson.
"You need to be a difference-maker," Islanders coach Jack Capuano said. "That's what we talked about. We talk about believability and trust and accountability, all the things that everybody else talks about. But at the end of the day, if you have a chance to succeed and win a Stanley Cup, your best players have to be your best players. Johnny's been there for us all year long."
Carlson tied it before the end of the first on the Capitals' third power play of the period. With Tavares serving a slashing penalty, Carlson took a pass from Ovechkin and beat Halak with a wrist shot from inside the right point with 4.3 seconds left to make it 1-1.
Islanders center Mikhail Grabovski nearly put the Islanders back in front midway through the second period. He sent a wrist shot from the slot that Holtby couldn't control, but the puck rolled inches wide of the goal post.
Halak kept the game scoreless with a save against Joel Ward less than five minutes into the first period. With the Capitals skating 2-on-1, Nicklas Backstrom sent a cross-ice feed to Ward, but Halak stretched across his crease to deny a one-time shot.
Capitals forward Jay Beagle nearly tied it with 5:33 left in the third period when his wrist shot hit the crossbar on a rebound chance. Replays confirmed the puck did not cross the goal line.
"We knew this was going to be the toughest game we played for sure," Carlson said. "I thought we did a good job coming out of the first period 1-1. [We] had a bunch of chances to make it 2-1 and their goalie played good and we didn't finish that well."
With de Haan and Visnovsky unavailable, defensemen Matt Donovan and Scott Mayfield made their NHL playoff debuts. Mayfield spent the entire regular season with Bridgeport of the American Hockey League. Right wing Colin McDonald played for the first time this postseason.
The Islanders are moving to Barclays Center in Brooklyn next season, and without a win Monday will have played their last game at their arena of 43 years.
"It was great to win in this building," Islanders forward Matt Martin said. "We don't want it to be the last one.
"It's been home to me my whole NHL career. It's the best atmosphere to play in. They don't really make them like this anymore."