New York (CNN) Donald Trump and Hillary Clinton notched resounding victories in New York Tuesday night, answering questions about their command of the race as the front-runners moved significantly closer to their party's nominations.

Their decisive wins usher in a new phase in the 2016 campaign. Both Trump and Clinton have fought bitterly for months to keep their rivals at bay, each slogging through primary contests that exposed vulnerabilities in their candidacies and campaigns.

On Tuesday, Trump came close to sweeping New York's 95 delegates -- a development that could help the Manhattan real estate mogul win the GOP nomination outright and avoid what would be an explosive and messy contested convention in July. Clinton's win, meanwhile, will go a long way in blunting the momentum of Bernie Sanders -- the liberal Vermont senator whose unexpected popularity has dogged the former secretary of state.

As of 12 a.m. ET, Trump held 847 delegates, while Ted Cruz had 553 and John Kasich had 148, according to CNN estimate. A Republican candidate needs 1,237 delegates to clinch the nomination.

Across the aisle, Clinton was leading with 1,930 delegates including 1,443 pledged delegates and 487 superdelegates. Sanders had a total of 1,223 delegates including 1,183 pledged delegates and 40 superdelegates. A Democratic candidate needs 2,383 delegates to secure the nomination.

It was a sweet homecoming for the front-runners, who each have deep ties to New York.

Last year, Trump and Clinton -- in wildly different settings -- launched their White House campaigns in New York City. On Tuesday, it was again in Manhattan that both Trump and Clinton confidently declared that they were within reach of the ultimate prize.

In a victory speech in the lobby of Trump Tower, Trump said Cruz was "just about mathematically eliminated."

"We don't have much of a race anymore," Trump boomed. "We're going to go into the convention I think as the winner."

His remarks suggested he may take a less harsh tone against his GOP competitors in the weeks ahead. While Trump slammed Cruz, he called him "senator" instead of his favorite nickname: "Lyin' Ted."

'Victory is in sight'

And at a midtown Sheraton Hotel just two avenues west, Clinton triumphantly told supporters that "victory is in sight."

JUST WATCHED Hillary Clinton's New York primary victory speech Replay More Videos ... MUST WATCH Hillary Clinton's New York primary victory speech 18:53

"We started this race not far from here on Roosevelt Island," Clinton said in her victory speech. "And tonight, a little less than a year later, the race for the Democratic nomination is in the homestretch and victory is in sight."

The biggest question for Trump going into the night was whether his margin of victory would be high enough to clinch most of New York's 95 delegates. CNN projects Trump will clear the 50% threshold to take all of New York's 14 statewide delegates. He will need to win majorities in each of the state's 27 congressional districts to win all of the remaining delegates.

With 93% of the vote in at 12:15 a.m ET, Trump was in the lead at 60% while Ohio Gov. John Kasich was at 25.2% and Texas Sen. Ted Cruz was at 14.8%.

With 94% of the Democratic vote in, Clinton was leading Sanders 57.7% to 42.3%.

JUST WATCHED Ted Cruz: Trump's campaign can't run a lemonade stand Replay More Videos ... MUST WATCH Ted Cruz: Trump's campaign can't run a lemonade stand 00:51

The New York GOP primary confirmed the voter sentiments that have propelled Trump's remarkable campaign. According to CNN exit polls, the billionaire businessman was the overwhelming favorite among Republican voters who said the next president should be "outside the establishment," as well as those who are angry at or dissatisfied with the federal government. More than 9 in 10 Republican voters who said a presidential candidate's top quality is to "tell it like it is" backed Trump.

In the Democratic contest, exit polls also showed that Clinton drew support from demographic groups that helped her in past races. She won 66% of voters 45 and older, while Sanders was the favorite among younger voters, 18-44. Clinton also once again dominated among minority voters, winning 75% of the African-American vote and 64% of the Latino vote.

Trump's New York victory came at a pivotal moment for the front-runner.

Over the past few weeks, Trump has come face-to-face with the Cruz campaign's strong command of the complicated delegate allocation rules. The GOP front-runner has expressed frustration as he's watched Cruz walk away with victories and increase his delegate pile -- a sentiment that boiled over after the Texas senator swept the Colorado Republican convention earlier this month.

Cruz, whose campaign acknowledged ahead of time that it may walk away from New York with zero delegates, delivered remarks in Philadelphia Tuesday night that sought to draw a contrast between himself and Trump and emphasize party unity.

JUST WATCHED Trump: Cruz is 'just about mathematically eliminated' Replay More Videos ... MUST WATCH Trump: Cruz is 'just about mathematically eliminated' 01:35

"I'm so excited to share with you what America has learned over the past few months, and it has nothing to do with a politician winning his home state," Cruz said, calling 2016 the "year of the outsider."

"We must unite the Republican Party because doing so is the first step toward uniting all Americans," he added. "Let us unite on the things that have always made us great."

Fearing that the magic number of 1,237 delegates needed to win the nomination was becoming increasingly elusive, Trump sanctioned changes within his operations ahead of the New York contest.

Across the political aisle, the New York race came after Sanders had won eight of the last nine Democratic contests -- a reality that the Vermont senator has repeatedly touted on the campaign trail.

"I think the Clinton campaign and the secretary are getting a little bit nervous," Sanders told CNN after last week's particularly combative Democratic debate in Brooklyn.

New York roots

Tuesday's contests were particularly significant for three of the candidates who have roots in New York.

Trump is a Queens native and Manhattanite whose famous last name is featured on real estate properties around the city. For Clinton, the race was something of a homecoming: she was a New York senator for eight years, owns a home in Chappaqua and her campaign headquarters is in Brooklyn. And while Sanders has represented Vermont on Capitol Hill for decades, he was born and raised in Brooklyn and has spoken fondly about his upbringing in the borough.

Clinton in particular appeared to delight in campaigning in the five boroughs in recent days. She kept a packed schedule that included riding the subway, drinking bubble tea and sampling dumplings in Brooklyn -- all part of an effort to tour the city and mingle with its residents in relatively casual settings.

Trump and Clinton spent Tuesday morning taking care of their first order of business: voting.

Trump visited his polling station, the Central Synagogue three blocks east of Trump Tower, where he cast a ballot for himself for the first time.

"It's a proud moment. It's a great moment. And who would've thought? It's just an honor," he told reporters.

New Yorkers in the spotlight

With so much at stake for the two front-runners, Empire State voters on were in the unusual position -- for the first time in decades -- of playing a crucial role in the presidential nomination process.

Local political figures in both parties relished the state's rare moment in the spotlight of a presidential election.

"It's been an unusual circumstance where New York is one of the deciding factors in the Democratic race, so that's exciting," said Democratic Queens Borough President Melinda Katz.

New York State Republican Party Chairman Ed Cox referred to the contests here as his state's "New Hampshire moment" -- a reference to the New England state's outsized role in the presidential primary.

"This is what the New York state party needs. We need this kind of excitement," Cox said. "We are indeed having our decisive moment in selecting the next president of the United States."