The winners of New York’s presidential primaries ran strongly on Long Island, beating their statewide margins amid high voter turnout.

Democrat Hillary Clinton, former secretary of state, took 63 percent of the vote in Nassau County — one of her best county performances. That was 5 points higher than her victory over Sen. Bernie Sanders of Vermont statewide.

In Suffolk, Clinton beat Sanders 55-to-45.

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Businessman Donald Trump’s domination of the Republican field got a big boost in Suffolk: He won with 73 percent in the county, 54 points over his closest competitor, Ohio Gov. John Kasich. Only Staten Island, where Trump got 82 percent, gave him a bigger margin.

Trump got more votes in Suffolk — 70,000 — than in any other county. Add the 67,000 he got in Nassau, and Long Island accounted for a quarter of his 523,000 votes statewide. Overall, Trump beat Kasich by 36 points, and Texas Sen. Ted Cruz by 46.

“We exceeded expectations all around,” said Suffolk GOP chairman John Jay LaValle, who had Trump headline a party fundraiser in Patchogue last week and stood behind him during his victory speech Tuesday night in Manhattan.

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Clinton got 71,000 votes in Nassau, beating Sanders by 25 points. Her statewide vote margin over Sanders was 16 percentage points.

“We worked very hard in Nassau. We had a whole independent operation in addition to what the campaign had,” said Nassau Democratic chairman Jay Jacobs, a prominent Clinton supporter who brought her to Port Washington for a campaign event and had her husband, former President Bill Clinton, rally local Democrats in Elmont.

Voters cast about 400,000 ballots in the Republican and Democratic primaries on Long Island Tuesday. For the GOP primary, turnout was 31 percent in Suffolk and 30 percent in Nassau.

On the Democratic side, 28 percent of eligible voters came to the polls in Suffolk and 30 percent voted in Nassau.

New York’s contested Democratic primary between Clinton and then-Sen. Barack Obama in 2008 drew turnouts of 37 percent in Nassau and 32 percent in Suffolk.

Republican turnout that year, when Arizona Sen. John McCain won the GOP nomination, was 20 percent in Nassau and 19 percent in Suffolk.

In 2012, when Republicans held the only primary in New York and former Massachusetts Gov. Mitt Romney had essentially secured the nomination by the time of the state’s primary, barely 5 percent of eligible voters cast ballots in each county.

“This tells you that there’s a lot of energy in both parties this year,” said Lawrence Levy, executive dean of Hofstra University’s National Center for Suburban Studies.

New York’s delegates to the parties’ nominating conventions were awarded largely based on congressional district totals, and Clinton and Trump’s victories on Long Island included significant margins in nearly all five districts that cover Nassau and Suffolk.

Sanders ran within 4 percentage points of Clinton in the 1st District on the East End. But Clinton won by 25 points in the 3rd and 4th districts, which are largely in Nassau.

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Trump received at least 66 percent in each Long Island-based congressional district and got 75 percent of the vote in the 2nd District, which is split between Nassau and Suffolk. Trump lost only 12 of Suffolk’s 1,052 election districts.

Trump’s dominance on Long Island gave LaValle hope that Trump can win New York State in a general election. That hasn’t happened since Ronald Reagan won re-election in 1984. “He’s lighting up people like never before,” LaValle said of Trump.

But Jacobs said “the model is very different in a general election.”

Nassau GOP chairman Joseph Mondello also expressed skepticism.

“I’m not going to take anything away from Trump. He did exceptionally well,” Mondello said. “It’s just that in reality, when you compare it to the Democrats and the way the state is set up, he’s got a long way to go.”