The event, held in Cleveland, Ohio, began in a civil manner, with the president striding deliberately to his lectern and Mr Biden nodding to his opponent and asking, “How you doing, man?”
But Mr Trump is no stranger to going on the offensive, with his aggressive manner leaving his opponent fighting to complete a sentence as he attacked in sometimes intensely personal ways.
“There’s nothing smart about you. Forty-seven years you’ve done nothing,” Mr Trump said, referring to his opponent’s time in Washington.
Mr Trump played up to his reputation as a bully and it may have been effective at breaking up the worst of his opponent’s attacks – simply by talking over them.
Trump aides believed before the debate that Mr Biden would be unable to withstand the withering offensive on style and substance from Mr Trump, but the former vice president came back with a few retorts of his own, calling Mr Trump a “clown” and mocking his style by asking, “Will you shut up, man?”
That was after the president badgered him over his refusal to comment on whether he would try to expand the Supreme Court in retaliation if Mr Trump’s high court pick, Amy Coney Barrett, was confirmed to replace the late Justice Ruth Bader Ginsburg.
Mr Trump struggled to define his ideas for replacing the Affordable Care Act on health care in the debate’s early moments and defended his nomination of Ms Barrett, declaring: “I was not elected for three years, I’m elected for four years.”
“We won the election. Elections have consequences. We have the Senate. We have the White House and we have a phenomenal nominee, respected by all,” he added.
— GOP (@GOP) September 30, 2020
Mr Biden called his opponent “the worst president America has ever had”, while Mr Trump recycled allegations about Hunter Biden’s international business practices.
The Democrat called the claims against his son “discredited” and fired back: “I mean, his family we can talk about all night.”
But Mr Biden sidestepped any of the specifics of the president’s international business dealings and instead turned straight to the camera.
He said: “This is not about my family or his family. This is about your family.”
Both candidates appealed to the families of voters watching at home as they addressed the pandemic.
“It is what it is because you are who you are,” Mr Biden told the president, referring to Mr Trump’s months of downplaying Covid-19 while he said privately he understood how deadly it was.
Mr Trump replied that the death toll would have been worse if his opponent were president, adding that the economy would also have suffered more.
The president said “there will be a vaccine very soon”, while Mr Biden fell back on his bottom line: “A lot of people died, and a lot more are going to unless he gets a lot smarter.”
Mr Trump again refused to say when he will finally make his personal taxes public as he has long promised, which followed a report in the New York Times suggesting he had paid only 750 dollars (about £583) in personal income taxes annually in recent years.
Trump downplayed and worsened the crisis. He failed to lead, and now over 200,000 Americans are dead. pic.twitter.com/Pb0r2rhkc0
— The Democrats (@TheDemocrats) September 30, 2020
Mr Biden quickly used that as a point of attack, saying Mr Trump “does take advantage of the tax code” and “pays less tax than a school teacher”.
Mr Trump shrugged off the attack, saying that all business leaders do the same “unless they are stupid”.
Meanwhile, the president danced around a question from debate moderator Chris Wallace about whether he was willing to condemn white supremacists and military groups.
He said: “Proud Boys — Stand back, stand by, but I’ll tell you what, somebody’s got to do something about Antifa and the left because this is not right-wing problem… This is a left-wing problem.”
Antifa followers have appeared at anti-racism protests, but there has been little evidence behind Republican claims that followers are to blame for the violence at such protests.
Asked if humans were partially to blame for environmental deterioration, the president replied: “To an extent, yes.”
But when he was asked why he took steps like withdrawing the US from the Paris climate agreement, Mr Trump repeated his argument that such pacts were “driving energy prices through the sky”.
Mr Biden said he would champion job-creating schemes that embrace green technologies and would rejoin the Paris accord, which is “all falling apart” without US involvement.
The debate ended with a question from the moderator, who asked both candidates if they would “urge your supporters to stay calm during this period, not to engage in civil unrest and will you not declare victory until the election has been independently verified?”
Mr Trump said he will tell his supporters “to go into the polls and watch very carefully because that’s what has to happen. I’m urging them to do it”.
Mr Biden replied: “Once the ballots are all counted, that’ll be the end of it. If it’s me, that’s fine. If it’s not me, I’ll support it.”