Immigration, healthcare and outreach to Latino voters dominated the debate, which disintegrated into long periods of shouting and personal insults.
Mr Trump has won three of the first four contests held so far.
Next week's vote in 11 states is held on what is known as Super Tuesday.
Analysis: Anthony Zurcher, BBC News North America reporter
At long last the Republican candidates have come to the realisation that Donald Trump can actually win this race, but it may be too late.
For more than two hours, Senators Marco Rubio and Ted Cruz took turns throwing punches at the New Yorker. They attacked him on his business record; they mentioned hypocrisy; they questioned his conservative credentials; and they criticised the lack of detail in his policies and his reliance on bluster.
"We're having a lot of fun up here, aren't we?" the front-runner quipped at one point. But the truth is that Mr Trump was on his heels for much of the evening.
The challenge for the men who would unseat the leader, however, is that the best time to bludgeon a candidate is before it is clear circumstances are forcing you to act. In a campaign where authenticity is worshipped above all, Thursday's fireworks could smack of the kind of political expediency many associate with traditional politicians.
Both Mr Cruz and Mr Rubio drew blood with their attacks but Mr Trump will be likely to emerge unbowed.
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Rubio's onslaught
Mr Rubio, who has come second in many of the recent contests, mounted a series of attacks on Mr Trump.
"If he hadn't inherited $200m, you know where Donald Trump would be?" Mr Rubio said in one tense exchange. "Selling watches in Manhattan."
Mr Rubio also criticised Mr Trump's failed online education venture, Trump University, and assailed him for hiring foreign workers rather than Americans in his construction projects.
Mr Trump shot back: "I hired tens of thousands of people. You've hired nobody."
The billionaire real estate mogul found himself increasingly on the defensive about his business dealings, his conservative credentials and his support for Israel.
In other exchanges
- Mr Cruz said Mr Trump's reputation as a dealmaker meant he could not be trusted to appoint conservative justices to the Supreme Court
- Most of the candidates were asked about releasing their tax returns; Mr Cruz and Mr Rubio pledged to release them in days, while Mr Trump demurred
- Moderator and Telemundo presenter Maria Celeste grilled Mr Trump on how he would appeal to Latino voters in the presidential election
- Mr Trump addressed criticisms from Mexico's former president, who said Mexico would never pay for a border wall between the two countries. "Mexico will pay for the wall," Mr Trump said. "The wall just got 10 feet taller"
- Ohio Governor John Kasich touted his successes in his state, including overcoming a budget deficit and bringing new industries
- Former neurosurgeon Ben Carson, struggling to participate, at one point called out: "Can someone attack me?"
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