The attacks turned personal as Republican Donald Trump accused his rival Hillary Clinton of not having the right temperament to be president.
Meanwhile, Mrs. Clinton baited Mr. Trump by pointing out that he refuses to release his tax returns.
The New York showdown could be the most watched debate in TV history, with up to 100 million viewers.
Hours before the programme, polls suggested the candidates were locked in a dead heat, adding to the tension between the rivals on stage throughout the debate.
“I have a feeling that by the end of this evening, I’m going to be blamed for everything that’s ever happened,” Mrs. Clinton quipped when prompted to respond to one of Mr. Trump’s attacks.
“Why not?” Mr. Trump interrupted.
“Yeah, why not,” she answered. “You know, just join the debate by saying more crazy things.”
Mr. Trump was later thrown on the defensive by moderator Lester Holt for not disclosing his tax returns.
He claimed he was under a “routine audit” and would release the document once the audit was finished.
But the hotel developer promised he would release them if his opponent released 33,000 emails that were deleted during an investigation into her private email set-up while secretary of state.
Mrs. Clinton made a brief response to Mr. Trump’s attacks about her use of a private email server – which has haunted her on the campaign trail.
She said there were no excuses for the “mistake” and that she takes responsibility for it.
But she was also uncomfortable when defending her changing position on the controversial Trans-Pacific Partnership trade deal.