Clinton took big strides toward the Democratic nomination by winning Florida and North Carolina. And in crucial victories, she stopped Bernie Sanders in his tracks in the industrial Midwest by taking Ohio and Illinois.
The Republican Party, meanwhile, veered closer to a contested convention after Kasich held his own state and deprived Trump of its 66 delegates. That makes it more difficult for the billionaire to reach the 1,237 delegates he needs to capture the GOP prize.
Trump did, however, prevail in the biggest contest of the night, taking all of Florida's 99 delegates. That resounding win helped force Rubio out of the race after failing to win his own state and unite the Republican establishment against Trump. The real estate tycoon also won primaries in Illinois and North Carolina.
"This was a great evening," he said. "This was an amazing evening."
The drama is still unfolding in other key races. Trump and Texas Sen. Ted Cruz are locked in a tight battle for Missouri. And Clinton is still hoping for a sweep, with votes still being counted in the close race with Sanders in Missouri.
Vote counting was completed for the night in Missouri
with both Clinton and Trump clinging to tight leads of less than half a percentage point, but CNN will not project a winner in either contest as the margin of victory in each case is less than 1 percentage point.
Trump was already looking forward to the general election as he urged party unity amid growing speculation about the potential for a convention fight.
"We have to bring our party together," he said. "We have to bring it together."
Still, GOP leaders may now look to Kasich as their final chance to unite behind a candidate who could challenge Trump in the event of a contested convention.
"We are all very, very happy," Kasich told CNN's Wolf Blitzer in a telephone interview.
According to CNN estimates, Trump needs to win about 60% of the remaining delegates available in the GOP race -- a goal complicated by the fact that some states award delegates on a proportional basis, rather than doling out their entire hauls to the winner, as is the case in Ohio and Florida.
But it's unclear how Kasich, a contender who has won only one state and who has been laboring in obscurity for much of the race, can overtake Trump, who has now won 18 states and is far ahead in the delegate race.
The billionaire, who has harnessed the anger of grass-roots Republicans against party elites, is responsible for destroying the campaigns of some of the GOP's most imposing personalities -- all of whom were once considered strong White House contenders, including Rubio, Jeb Bush and Chris Christie.
Democrats battle it out
On the Democratic side, Clinton has won the Illinois, North Carolina, Florida and Ohio primaries -- crucial victories that bolster Clinton's claim that she is her party's only candidate who can win diverse states that will be pivotal in the November general election.
Her win in North Carolina completed her sweep of Southern states, where she has enjoyed strong support from African-American voters.
"We are moving closer to securing the Democratic Party nomination and winning this election in November," Clinton said in a victory speech in West Palm Beach, Florida.
Clinton said that by the end of the night, she would have two million more votes than Sanders, and hold a lead of more than 300 in the delegate count. While Clinton did not urge Sanders to quit the race so she could turn her fire on Trump, her comments appeared to be a gentle message to her stronger-than-expected challenger.
Clinton's victory in Ohio follows her surprise loss in Michigan last week, which raised fresh questions about her campaign strategy and provided a lift to Sanders that he hoped would help him sweep the Midwest. That loss may ultimately turn out to be an anomaly given her wins in Illinois and Ohio.
She unveiled a retooled message in her victory speech that simultaneously rationalized her campaign against Sanders and foreshadowed a general election duel with Trump, as she stressed repeatedly she would create jobs as president and stand up for the middle class.
"We are going to stand up for American workers and make sure no one takes advantage of us -- not China, not Wall Street, not overpaid corporate executives," she said.
Clinton's victories on Tuesday give Sanders a tough climb if he is to grab the nomination.
He would need to win about 72% of the remaining delegates in order to do so, according to CNN estimates, and time may be running out for him unless he can start racking up huge victory margins in coming state contests. Still, most Democratic strategists expect Sanders to stay in the race for several months.
Rubio drops out
With Rubio's decision to drop out, three Republican candidates remain in the White House race -- Trump, Kasich and Cruz.
In a speech that served as a thinly-veiled rebuke of Trump's campaign tactics, Rubio warned that the politics of division will leave America a "fractured nation."
"America is in the middle of a real political storm, a real tsunami and we should have seen this coming," Rubio said. "While we are on the right side," he said, "this year, we will not be on the winning side."
Rubio spent the final weeks of his campaign in an often bitter fight with Trump. But on Tuesday night, Trump congratulated the Florida senator "for having run a tough campaign."
"He is tough," Trump said. "He is smart and he has got a great future."
Cruz also praised Rubio warmly, saying he could "paint a picture and weave a tapestry about the promise of America like nobody else."
And Cruz told Rubio's bereft supporters: "We welcome you with open arms."