New York Islanders' Brock Nelson, second from left, celebrates with...

New York Islanders' Brock Nelson, second from left, celebrates with teammates after scoring during the first period of an NHL hockey game against the Toronto Maple Leafs in Toronto, Tuesday, Dec. 29, 2015. Credit: AP / Chris Young

TORONTO — Jack Capuano said before Tuesday’s game he hoped the Islanders sizable contingent of Toronto-area natives could play well in front of family and friends.

They did. So did Islanders from Denmark, Minnesota, Germany and wherever else they’re all from.

The 6-3 win over the Leafs was a much more complete effort than Sunday’s 3-1 loss to the same team down in Brooklyn, not necessarily a dominating performance by the Islanders but an effective one as they scored their six goals on 15 shots over the first two periods.

“We were pretty well in control from the beginning,” said Josh Bailey, whose pretty feed produced John Tavares’ first goal in six games to put the Isles ahead 2-1 at 11:51 of the first. “All 30 teams go through games like we had [Sunday], but we’ve been able to put those games behind us by the next day’s practice or the next game.”

Capuano was specifically referring to Tavares, a native of nearby Oakville who has played well in the Air Canada Centre — his goal and a second-period assist on Anders Lee’s goal gives the Islanders captain 15 points in his last seven games here.

Frans Nielsen also had a goal and assist and his speed rush through the Leafs made it 3-1 late in the first. Toronto cut its deficit to 3-2 at 10:57 of the second on a score by former Islander P-A Parenteau, but Nielsen stole the puck from Leafs goaltender Jonathan Bernier and fed ex-Leaf Nikolay Kulemin for an open-netter just 28 seconds later.

Matt Martin and Lee scored 74 seconds apart in the final 1:54 of the second to completely dim the home crowd — save for the sections of Tavares, Casey Cizikas, Ryan Strome and Cal Clutterbuck supporters.

Lee’s goal snapped a 15-game goalless slide and, even though it was the sixth goal in a rout and needed to withstand a Toronto coach’s challenge, was a load off Lee’s mind.

“It felt good to get a bounce, finally,” Lee said. “After Sunday we needed to come back even harder against a good team that took care of us. We did that pretty well.”

Thomas Greiss made 30 saves, including 12 in that middle period when the Isles got a bit shaky. Bernier was pulled after two periods.

The Islanders head to Buffalo with another chance to build off a stronger outing, as happened when they downed the Ducks just before the holiday break.

“The positive thing is we know we can still be better,” Martin said. “We have enough confidence to bounce back from a bad game and now we need to build off it.”

Notes & quotes: Brad Boyes, another former Islander, had a goal and assist for the Leafs. Brock Nelson scored the opening goal of the night for the Isles, who matched their season high for goals from Oct. 17 . . . Marek Zidlicky replaced Brian Strait in the lineup on Tuesday. Jaroslav Halak (upper body) remained behind on Long Island as Greiss won for the 10th time this season.

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