Trump, leading polls in South Carolina and in position to take command of the Republican nomination fight if he wins the state's Republican primary on Feb. 20, attacked Bush's brother, former President George W. Bush, for invading Iraq in 2003 over weapons of mass destruction that were never found.
The raucous back-and-forth was the most bitter exchange between the two men over the course of nine debates and was a sign of how critical both see a strong showing in South Carolina.
"George Bush made a mistake," Trump thundered. "We all make mistakes. But that one was a beauty ... They lied! They said there were weapons of mass destruction. And there were none."
As many in the crowd booed Trump, the billionaire Republican front-runner dismissed them as "lobbyists and special interests" who supported Jeb Bush, the former Florida governor.
Bush also criticized Trump for remarks praising Russian President Vladimir Putin, saying Putin is stirring turmoil in Syria by launching air strikes in support of Syrian President Bashir Assad, who Washington would like to leave power.
Bush, who will campaign on Monday with his brother George, rejected Trump's comments and defended his family.
"I'm sick and tired of him going after my family," Bush said. "My dad is the greatest man alive in my mind. While Donald Trump was building a reality TV show, my brother was building a security apparatus to keep us safe. And I'm proud of what he did."
"He had the gall to go after my mother," Bush said, reminding the audience that Trump had criticized his 90-year-old mother, Barbara Bush, wife of former President George H.W. Bush. for him. "My mother is the strongest woman I know."
"She should be running," Trump responded.
Before the Trump-Bush fight, the Republican candidates urged President Barack Obama not to nominate a successor to the late Supreme Court Justice Antonin Scalia, saying it should be up to the next president to decide.
Scalia's death, announced earlier on Saturday, and the consequences for the conservatives' 5-4 advantage on the high court cast a shadow over the ninth debate between rivals for the Republican presidential nomination for the Nov. 8 election.
"I would like the president for once here to put the country first," Ohio Governor John Kasich said at the outset of the two-hour debate hosted by CBS. "We're going to have an election very soon ... I think we should let the next president of the United States decide."
Obama, speaking shortly before the debate began, said he planned to nominate a successor to Scalia and said the US Senate should give the nominee careful consideration.
The Republican candidates were unanimous in saying Obama should put off a decision. Trump said Senate Majority Leader Mitch McConnell should ensure that any Obama nominee is blocked from confirmation.
"Delay, delay, delay," Trump said.
