The emphatic wins give Clinton and Trump edge over their rivals Bernie Sanders and Ted Cruz and solidify their front-runner status after a series of losses recently. It also resoundingly answers questions about their command of the White House race.
Trump's win means he could sweep the state's 95 delegates and position himself to win the Republican nomination without going through a contested Republican convention in July.
With 98 per cent of the vote in, 69-year-old Trump was in the lead at 60.5 per cent while Kasich was at 25.1 per cent and Cruz at 14.5 per cent.
With 98 per cent of the Democratic votes in, Clinton was leading Sanders 57.9 per cent to 42.1 per cent.
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Trump's big victory in his home state gave him renewed momentum in the Republican race and pushed him closer to the 1,237 delegates required to win the nomination.
Across the aisle, Clinton was leading with 1,930 delegates including 1,443 pledged delegates and 487 super-delegates. Sanders had a total of 1,223 delegates including 1,183 pledged delegates and 40 super-delegates.
A Democratic candidate needs 2,383 delegates to secure the nomination.
"Today you prove once again there is no place like home...This win is personal," said the 68-year-old former secretary of state, joined by her husband ex-president Bill Clinton and daughter Chelsea, in her victory speech. "The race for the Democratic nomination is in the home stretch and victory is in sight."
"We are about lifting each other up, not tearing each
other down. Our country is at its best when we come together -- no one knows that better than New Yorkers," Clinton said.
In a passing reference to Sanders, Clinton said it was not enough to just diagnose the problem. "America is a problem-solving nation. We have set progressive goals for creating more jobs and providing dignity and pride," she said.
Sanders in a tweet said that he was looking ahead to the five northeast states that vote on April 26.
"Thank you to all those who came out tonight in New York! Onward to five more states voting next week," he tweeted.
Trump also appeared like a different candidate in his victory speech at his Trump Tower in Manhattan. His speech focussed on jobs and trade and the economy but did not mention Clinton.
"We don't have much of a race anymore," Trump said to applause and cheers from his supporters. "Sen Cruz is just about mathematically eliminated."
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Political pundits here believe, Trump despite having the largest number of delegates in his kitty is still far short of the magical figure of 1,237 delegates he needs to have before the Cleveland convention in July to become the Republican presidential nominee.
Trump, is now eyeing at the Republican primaries next Tuesday's in the States -- Maryland, Pennsylvania, Connecticut, Delaware and Rhode Island -- where 172 delegates are at stake.
Well aware of the high stakes in these States, the Republican front runner is scheduled to campaign heavily in these States.
Even if he does not do so, in all likelihood he would enter the July Convention with the largest number of delegates.
The entire strategy of Trump's two remaining rivals Cruz from Texas and Ohio Governor Kasich is to prevent Trump from hitting the target of 1,237 delegates.
By doing do, the Cruz and Kasich campaigns hope that given Trump's rhetoric and his antipathy with the establishment, the delegates would vote against the New York thus opening up opportunities for them.
Clinton now has 502 super delegates, who are mainly party officials, have pledged their support to her. But they can change their vote even at the last moment.
Sanders campaign believes that they can still manage to get the necessary delegates in the rest of the States to win the party's nomination.
Latest polls show, Clinton is leading in most of the Democratic primaries to be held in States of Maryland, Connecticut, Delaware, Pennsylvania and Rhode Island.