Both secured multiple primary victories , which make it more improbable that their rivals can catch them in their respective party’s presidential nomination contests.
The socialist candidate had hoped to capitalise on a surprise win last week in Michigan , but held a slim lead in Missouri.
Trump also won North Carolina and Illinois, overcoming a wave of attack ads and negative publicity over his campaign rhetoric and violent disturbances at rallies.
But the billionaire businessman was soundly defeated in Ohio by John Kasich, in his first victory so far in the race.
Super Tuesday III proved a pivotal day for Trump and Clinton, as they each looked for enough victories to make their paths to the nomination unstoppable.
Speaking to supporters in Florida, Clinton turned her attention to Trump, saying: “To be great, we can’t be small. We can’t lost what made America great in the first place.”
Rubio was hoping that he could upset in his home state, where Trump had a significant lead in most polls.
As the youngest candidate in the race, Rubio was once viewed as someone who could unite factions of the GOP, while he pitched his campaign as a forward-looking contrast to Jeb Bush and Hillary Clinton.
In fact, many Democrats saw Rubio as Clinton’s most formidable potential rival.
“While this may not have been the year for a hopeful and optimistic message about our future, I still remain hopeful and optimistic four our country,” Rubio said in conceding.
He said that “America is in the middle of a real political storm, a tsunami, and we should have seen this coming.”
Analysts in recent days have said that if Kasich were to deny Trump a victory in Ohio, there would be a good chance that no GOP candidate will have a majority of delegates by the time of the Republican National Convention in July.
Such a prospect has not played out in either party since 1976, when President Gerald Ford was challenged by Ronald Reagan.
But Ford won the nomination on the first ballot, in a race that didn’t have the powder-keg of anger and grievance playing out this year.
In Ohio, Kasich told supporters, “I will not take the low road to the highest office in the land.” It was a reference to how he has avoided getting into an insult-laden back-and-forth with Trump.
“We are going to go all the way to Cleveland and secure the Republican nomination.”
His best chances appear to hinge on a contested convention.
Trump has been criticised by rivals in the last few days for stoking anger and even violence at his rallies, along with a battering of attack ads chiding him for his rhetoric and past statements on women and minorities.
“No one in the history of politics has received the kind of negative advertising I have. Record, record, record,” Trump said at an event at his Mar-a-Lago resort in Palm Beach, Fla.
Instead, “My numbers went up. I don’t understand it.”