Moderator Lester Holt struggled to rein in the candidates, with discussions about trade policy.
After greeting each other with a handshake and a smile, the two opponents went on the attack, with Clinton calling the New York businessman's tax policies "Trumped-up trickle-down" economics and Trump accusing the former secretary of state of being "all talk, no action."
Each accused the other of distortions and falsehoods and urged viewers to check their websites for the facts. She called him Donald, and he called her Secretary Clinton
"I have a feeling I'm going to be blamed for everything," said Clinton, the first woman to win the presidential nomination of a major U.S. political party.
"Why not?" Trump retorted.
As the debate opened, they put forward competing visions for the U.S. economy.
"The kind of plan that Donald has put forth would be trickle-down economics all over again. And in fact it would be the most extreme version, the biggest tax cuts for the top percents of the people in this country that we've ever had," Clinton said. "I call it Trumped-up trickle-down, because that's exactly what it would be."
Trump, a real estate tycoon and former reality television star who has never held elective office, criticized Clinton for her trade policies and said she would approve a controversial trade deal with Asian countries despite opposing it as a candidate.
"You were totally in favor of it, then you heard what I was saying, how bad it is, and you said, 'Well, I can't win that debate,' but you know that if you did win, you would approve that," he said.
Clinton rejected the criticism.
"Well Donald, I know you live in your own reality, but that is not the facts," she said.
Clinton, 68, wore a red pantsuit, and Trump, 70, wore a dark suit and a blue tie to the encounter that could shift the course of the tight 2016 race for the White House.
Moderator Lester Holt struggled to rein in the candidates, with discussions about trade policy suddenly shifting to the fight against Islamic State as Trump accused Clinton of giving away information to the enemy by revealing on her website how she planned to defeat the group.