The lively showdown between the two very different candidates included an exchange where Clinton accused Trump of not releasing his tax returns because this would reveal he had not personally paid any income tax in recent years.
But Trump interrupted saying “that makes me smart” and later added that he would release his returns if Clinton would show the world 33,000 deleted emails from her time as US secretary of state.
Clinton said perhaps Trump was not as rich or as charitable as he said and that “he is probably not all that enthusiastic about having the rest of the country see because it must be something really important, even terrible that he is trying to hide”.
The debate was watched by up to 100 million viewers.
The latest polls put Clinton ahead with 48% of the vote, and Trump on 46%.
US presidential candidate Hillary Clinton last week proposed raising inheritance tax paid by ultra-rich Americans to 65% on property valued at more than $500m (£385m, €445m), in a bid to appeal to the supporters of her former Democratic rival, Bernie Sanders.