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8 year oldDemocratic Virginia Senator Tim Kaine and Republican Indiana Governor Mike Pence clashed on a series of topics ranging from abortion to Russia.
But they focused their sharpest exchanges on Mrs Clinton and Mr Trump.
The running mates tangled at Longwood University in Farmville, Virginia, 34 days before Americans go to the polls.
It set the stage for a second presidential debate this Sunday in St Louis, Missouri, where Mr Trump needs to rebound from a wobbly performance in the first match.
In Tuesday's 90-minute duel, the usually low-key Mr Kaine went on the attack from the beginning.
But while the two frequently talked across each other, Mr Pence seemed imperturbable.
Mr Kaine invoked Republican President Ronald Reagan when talking about the dangers of nuclear weapons under a Trump presidency.
He said Mr Reagan had once warned that nuclear proliferation could lead to "some fool or maniac" triggering a "catastrophic event".
Mr Kaine said the Republican commander-in-chief had been referring to someone like Mr Trump.
The 58-year-old senator also criticised Mr Trump's temperament, saying he "can't start a Twitter war with Miss Universe without shooting himself in the foot".
In one of the more heated moments, Mr Kaine sharply criticised Mr Trump's complimentary remarks about Russian President Vladimir Putin.
Mr Trump praised dictators, said Mr Kaine, and had a "personal Mount Rushmore" made up of Mr Putin, Kim Jong-un, Saddam Hussein and Muammar Gaddafi.
"If you don't know the difference between dictatorship and leadership, then you've got to go back to a fifth-grade civics class," Mr Kaine said.
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But 57-year-old Mr Pence contended Mr Putin would respect Mr Trump because of his strength, "plain and simple".
He added that "the small and bullying leader of Russia has been stronger on the world stage than this administration - that's stating painful facts".
That's not an endorsement of Mr Putin, he said. "That's an indictment of the weak and feckless leadership of Hillary Clinton and Barack Obama."
It was a scattershot debate, and at times the subjects changed so jarringly it felt like the speed round of a game show. In the end, however, Mike Pence did what he had to do.
The Republican vice-presidential nominee's goal was to reassure Republicans panicked by Donald Trump's debate performance last week and his bungling in the days that followed that cooler heads will prevail. He did that.
His calm, steady style - honed over years as a talk show host - stood in marked contrast to Democrat Tim Kaine's over-caffeinated demeanour and rapid-fire attacks.
At times, of course, it seemed like Mr Pence was talking about a Donald Trump who doesn't exist - one who doesn't have a year-long history of inflammatory statements and controversial stands. And Mr Kaine was quick to call him on it.
Mr Pence's accomplishment, however, was to defend his traditional conservatism and make the case to wandering Republicans - particularly educated suburban voters - that they still have a home in the party. On Tuesday night, Mr Pence stopped the bleeding.
At best, however, he has turned the page on a disastrous week and given Mr Trump an opportunity to get back in the race. It is up to him to make the most of it.
The two candidates also clashed on Mr Trump's tax arrangements, which have come under scrutiny in recent days.
The property tycoon has refused to release his tax returns, but the New York Times reported he may have avoided paying taxes for the last 18 years.
Mr Pence said his running mate had "used the tax code just the way it's supposed to be used, and he did it brilliantly".
Mr Kaine shot back: "I guess all of us who do [pay taxes] are stupid?"
In other debate highlights:
The debate was hosted by CBS News' Elaine Quijano and followed last week's presidential debate, which drew a record 84 million viewers, according to Nielsen.
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