As of early Wednesday, Trump had 61 percent of the GOP vote in Tuesday's primary to 25 percent for Ohio Gov. John Kasich and 12 percent to Texas Sen. Ted Cruz, according to NBC News. Clinton had 58 percent to Vermont Sen. Bernie Sanders' 42 percent.
In the race for 1,237 delegates needed for the Republican nomination, Trump has 844 to Cruz' 559 and Kasich's 146. Clinton's victory pushed her to 1,885 of the needed 2,383 Democratic delegates to Sanders' 1,190, NBC News said.
Trump delivered a confident victory speech, celebrating his success and discounting his rivals' chances.
"We're going to end at a very high level and get a lot more delegates than anybody projected, even in their wildest imagination," the real estate tycoon said at the top of his Tuesday evening victory speech to enthusiastic chants of "U.S.A."
Pointing out his fellow businessmen in the crowd of supporters, including billionaire Carl Icahn, Trump hit on some of his campaign's biggest promises.
GOP front-runner Donald Trump, his wife Melania Trump and billionaire investor Carl Icahn on Tuesday night. Credit: Scott Wapner.
During her victory speech, Clinton said voters had proven that "there's no place like home," and boasted that her campaign had won in every region of the country. "From the north to the south to the east to the west, but this one's personal," the former U.S. senator from the Empire State said.
Although delegate math appears to favor her campaign, Clinton stopped short of declaring all-out victory on Tuesday, saying that "the race for the Democratic nomination is in the home stretch and victory is in sight."
Ahead of the contests, statewide polls indicated that Clinton and Trump were both likely to win their parties' primaries in New York. But before polls closed, exit polls offered some insight into the opinions of voters turning out on Tuesday.
On the nature of this year's race, only 39 percent of surveyed GOP primary voters said they thought it had energized their party. Instead, 57 percent reported that the Republican campaign had divided their party. And on the Democratic side, 68 percent said the race had energized their party, while only 27 percent thought the campaign had divided it, according to NBC.
And on the direction of the U.S. economy, voters in both primaries said they were concerned. Sixty-seven percent of surveyed GOP voters said they were "very worried" and 25 percent said they were "somewhat worried." Democrats, meanwhile, registered 46 percent in the "very worried" category, and 39 percent "somewhat worried," NBC reported.
Another interesting early exit poll question showed that a majority of both Democratic and Republican (64 and 51 percent, respectively) voters thought that Wall Street hurts the U.S. economy, NBC News reported.
But Sanders, speaking to a crowd in Pennsylvania before the New York polls closed, predicted that "we're going to do a lot better, I think, than people thought we would." In fact, Sanders said earlier this month that he "will win a major victory here in New York."
On the Republican side, Queens-born Trump has long been tied to the New York real estate market. The businessman had averaged about a 30 percentage point lead over Kasich.
Cruz of Texas, who bested national front-runner Trump in several states, had usually polled behind Kasich in New York polls ahead of the primary.
But the chance of a contest convention looms over the Republican race. In the New York GOP primary, 72 percent of voters said they thought the candidate with the most votes should become their party's nominee. Only 25 percent, according to NBC News, said the delegates should choose the party standard-bearer in the general election.
"We don't have much of a race anymore, based on what I'm seeing on television," Trump said during his victory speech, adding that "Senator Cruz is just about mathematically eliminated."
On the subject of general election viability, early exit polls showed that only 8 percent of New York GOP primary voters said that was the most important quality in a candidate. Instead, 35 percent said their chief concern is a candidate who can "bring needed change," and 28 percent said they cared most about picking someone who "shares my values," according to NBC News.
The next primaries are Tuesday in Connecticut, Delaware, Maryland, Pennsylvania and Rhode Island.