Their confrontations -- which played out as the candidates appeared on stage one-by-one -- underscored the intensity of the GOP contest heading into Saturday's South Carolina Republican primary. On Thursday night, Donald Trump, John Kasich and Jeb Bush will appear in a second town hall.
Cruz said that he "laughed out loud" when he learned of the cease-and-desist letter Donald Trump's campaign sent his team for running an ad highlighting his opponent's former position on abortion rights.
Cruz, Trump's closest rival in the state, defended the ad in question, saying it largely uses Trump's "own words" to demonstrate the businessman's past stance in favor of abortion rights.
"It is quite literally the most ridiculous theory I've ever heard, that telling the voters what Donald Trump's actual record is is deceitful and lying," he told moderator Anderson Cooper.
Rubio, who preceded Cruz, spoke in poignant personal terms about race and growing up as a Cuban-American.
The Florida senator said that as a young child, he was "disturbed" when his family was taunted by kids in the neighborhood.
"Some of the neighborhood kids, older kids, one day were taunting my family, saying, 'Why don't you go back on your boat? Why don't you go back to your country?'" he recalled.
Nevertheless, his parents "never raised us to feel that we were victims," Rubio said. "That doesn't mean I don't deny that there are people in this country that have had a different experience, and we need to recognize that."
Rubio also described his experience being color blind.
The two men, both of Cuban descent, did find common ground in denouncing President Barack Obama, however. Word emerged during the town hall that the President would be traveling to Cuba next month.
"He's allowing billions of dollars to go to tyrants who hate America," said Cruz, long a critic of Obama's Cuba policy. He said that the President was going to go to the island nation "and essentially act as an apologist."
Rubio, for his part, said that if he were president, he would not follow Obama's lead and visit Havana -- unless it were a "free Cuba."
But primarily the candidates focused on differences and attacks on one another.
Cruz hit Trump for alleging that the country was not safe under President George W. Bush's watch given the terrorist attacks of September 11, 2001, during his first year in office.
"I though it was ridiculous," Cruz said. "I thought it was really painful."
And he addressed a question from the audience about another allegation that Trump has thrown his way: that Cruz may not be eligible to be President of the United States because there is a question over whether he's a "natural-born citizen," as required by the Constitution.
"I've never breathed a breath of air on this planet when I was not a U.S. citizen," said Cruz, who was born in Canada. "It was the act of being born that made me a U.S. citizen."
Asked by Cooper to address Trump's recent threats to sue Cruz over the birthplace issue, Cruz joked that one can "never write off the possibility of Donald Trump suing you."
"There will still be some who try to work political mischief on it, but as a legal matter, this is clear and straightforward," he said. "He is welcome to file whatever lawsuit he likes -- that lawsuit would not succeed."
Rubio and Cruz spent the day ahead of the town hall sparring on the campaign trail. At the beginning of the forum, Rubio defended accusing Cruz of lying on the campaign trail.
Rubio doubled down on the charge, saying there is simply "no other word" for his rival's behavior.
"It's about your record, you've gotta clear it up," he said. "These things are disturbing and they need to be addressed."
Rubio insisted, however, that his escalating feud with Cruz was "not the core of my campaign."
Cruz later said, "Both Donald Trump and Marco Rubio are following this pattern -- that whenever anyone points to their actual record ... they start screaming liar, liar, liar."
Rubio, for his part, laughed off Cruz's comment earlier in the day that Rubio was acting like "Donald Trump with a smile."
"I don't know, this back and forth is silly," Rubio said at the town hall. "Ultimately it's not about me, it's not about Ted, it's not about Donald. It's about what is this country going to look like when my 15-year-old graduates from college."
Facing a contest in a state with a large military and veterans populations, Rubio, who sits on the Senate intelligence committee, also claimed that "no one running as a Republican has shown better judgment or has more experience on national security or on foreign policy than I do."
Asked to address former Florida Gov. Jeb Bush's criticism that Rubio lacks foreign policy experience -- and concerns about electing a first-term senator to the White House -- Rubio called Obama a "failed president."
"He is worse in his seventh year than he was in his first," he said. "His ideas don't work."
Before Rubio, Ben Carson took the stage and said that if he were president in his last year of office, he would nominate someone to replace late Supreme Court Justice Antonin Scalia.
"I probably would take the opportunity to nominate someone. Doesn't necessarily mean that person will be acted on or confirmed," Carson said, ahead of the Palmetto State's Republican primary on Saturday. "Why not do it?"
The retired neurosurgeon also weighed in Apple and the San Bernardino mass shooting.
"Apple and probably a lot of other people don't probably necessarily trust the government these days," Carson said, pushing for a "public-private partnership."
It's a "matter of people learning to trust each other," Carson added, saying Apple should "sit down with trustworthy members of the government."
Carson has struggled to regain his footing after briefly surging in the polls months ago. The political newcomer has particularly stumbled over national security and foreign policy questions -- critical issues in a state that has a large military and veterans community.
One questioner put Carson on the spot by asking what qualifications he has to be the country's commander in chief, particularly in light of the growing threat of ISIS and instability in the Middle East.
Carson responded that he was prepared for the job, repeating a line he frequently uses on the trail: that he has had to take more 2 a.m. phone calls than anybody else in the race.
"It's the political class that has tried to convince everybody that they're the only ones who can solve our problems," he said. "What we really need are people who know how to solve problems -- not people who know how to talk."