ABC's Martha Raddatz began the debate along with CNN's Anderson Cooper with first question by a teacher from the audience who asked if the two were modelling appropriate behaviour for the U.S. children.
Clinton in her response promised to work "with every American" and said she "will be the president for all Americans".
Still early in the debate, so a cautious Trump was found agreeing "with everything she said".
Coming to the video leaked by the Washington Post, Cooper said: "You bragged that you sexually assualted women -- do you understand that?"
Trump, tried his best to defend his lewd comments about women in the 2005 tape, saying: "No that's not what I said. This was locker room talk. I am not proud of it."
He then pivoted to terrorism and "bad things happening" in the world.
Taking on Trump, Clinton said though she had differences on policies and principles with the Republican candidates in the past, but Trump "was not fit to be president and commander in chief".
"We've seen him rate women on their appearance, ranking them from one to 10. It's not only women; it's not only this video... This is who Donald Trump is," she added.
Trump then accused Bill Clinton of doing much worse than just talking about sexual assault and even targeted the candidate of harassing a rape victim.
Clinton then mentioned other moments that damaged Trump's campaign, including a spat with Gold Star Parents, the Khans, while the billionaire accused her of starting the birther claim and said she should apologise to President Barack Obama.
Trump also mentioned WikiLeaks' disclosures of internal emails from Democrats.
Meanwhile, the Republican was hassled by the fact that his rival was getting more time to respond and that the moderators were not bringing up issues related to Clinton.
Trump said: "If I win, I am going to instruct my Attorney General to get a special prosecutor to look into your (email) situation... you ought to be ashamed of yourself."
There was also a moment when Trump insisted Clinton to answer the question about healthcare.
Clinton called reining in the cost of the Affordable Care Act the highest priority of the next president and agreed that premiums were high, but Trump said: "Obamacare will never work. It's very bad health insurance."
He insisted that it was too expensive and said he would repeal it.
When asked by a young woman in crowd about Muslims in the US being targeted and facing hate, Trump said: "She (Clinton) won't say the name, and Obama won't say the name, but the name is there: 'Radical Islamic terror'."
"Muslims have to report it when they see hate going on. Muslims have to report the problems when they see them," he added.
On his proposed Muslim ban, the Republican said it was the "greatest Trojan horse" of their time.
He said: "I don't want to have hundreds of thousands of people coming in from Syria when we know nothing about their values, their love for our country."
Clinton later called out Trump for denying his support for the war in Iraq to which Trump immediately interrupted and said that he was always against the war in Iraq.
When asked about candidate tax plans, Clinton attacked Trump referring to a New York Times report that he could have avoided federal income taxes for 18 years.
Trump said: "I pay tax, and I pay federal tax, too."
Replying to a voter's question, whether the candidates will be a devoted president to all people, Trump noted African-Americans, the inner cities and Latinos.
He cited a remark Clinton made, saying that half Trump's supporters are a "basket of deplorables".
Clinton said she had tried her entire life to do what "I can to support children and families".
When Cooper pressed Trump about his early hours Twitter rant against former Miss Universe Alicia Machado, the billionaire deflected and began talking about Clinton and Benghazi.
Referring to the early morning tweet about a sex tape, he said: "I'm not unproud of it."
He brought up the 2012 attack on the U.S. consulate in Libya, saying Clinton ignored multiple requests for more security from the U.S. ambassador who was killed in Benghazi.
Commenting on the war in Syria, Clinton said would specifically target the Islamic State leader Abu Bakr al-Baghdadi, while Trump mentioned: "I don't like Assad at all, but Assad is killing the IS. Russia is killing the IS and Iran is killing the IS, and the three have lined up together."
On Supreme Court Clinton said that she wanted to appoint judges "who understand the way the world really works" and that she wanted to protect voting rights, women's reproductive rights as well as marriage equality.
In the last question about naming one positive thing that the candidates respect in one another, Clinton said she respects Trump's children.
Trump, in return, said he respected that Clinton "doesn't give up" and the candidates, thus, signed off with a handshake.
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