The 26-year-old lunged at the line to pip Britain's Matthew Hudson-Smith, who set a new European record of 43.44sec, with Zambia's Muzala Samukonga taking bronze in 43.74sec.
For the first time ever five athletes went below 44 seconds in the same race.
Hall is the first American man to win the one-lap event at the Olympics since LaShawn Merritt in Beijing in 2008.
"I don't give up, man," said Hall. "I just got grit. I grind. I got determination.
"Anything that I can think of, that's what gets me to that line. I think of all the hurt, all the pain."
Hall, who said he thought of his two daughters as he crossed the line, said the grit came from the conditions in which he had studied as a young man.
"That's where that grit comes from," he said.
"When you have no food, you got to get your own food. No cafeteria, no study hall, none of that."
Hall timed his run perfectly, coming from nowhere to just get the better of Hudson-Smith, who had led off the bend and looked set to become the first British winner of the title since Eric Liddell at the Paris Olympics a century ago.
"It means a lot," said Hall, who was only a bronze medallist at last year's world championships. "Last year I told you guys I was going to get a better medal this year.
"Guess what? I got one gold."
'I cannot complain'
Just as in last year's world final in Budapest, Hudson-Smith tied up as he closed in on the line and again had to settle for silver.
The 29-year-old burst into tears as he walked around the track and spotted his parents whom he did not even know had travelled from Britain to watch him. His father hugged him and his mother wiped away his tears.
"I said if you're going to take it from me, or if you're going to win, you've got to take it from me," said Hudson-Smith.
"That's exactly what he did. I can't complain. Fifth fastest time overall.
"I cannot complain. I knew the last 50 will determine who wins and he got a step on me just before the line."
Hudson-Smith, who has made a remarkable comeback from being in the depths of despair three years ago when he contemplated taking his own life, predicted that he and Hall were set for some great clashes in the years to come.
"This will be the start of a lot of battles," the Briton said.
Samukonga, who denied Hudson-Smith the Commonwealth Games gold in 2022, also produced a storming finish to become only Zambia's third Olympic medallist and first since Samuel Matete's silver in the men's 400m hurdles in 1996.
"It's crazy," said the 21-year-old. "Competing at the Olympics, it has been my dream since the time I discovered that I'm an athlete, I can run.
"It means a lot to me. It's not an easy thing, first time competing at the Olympics.
"Then finding myself in the medal bracket, it's not an easy thing. I'm proud of myself."
The 2012 Olympic champion Kirani James had looked in sublime form in the rounds but in the final the 31-year-old's legs weakened entering the straight and he finished fifth in 43.87sec.
James said he had never thought he would see a race to rival the 2016 final in Rio when he took silver as Wayde van Niekerk won and set the world record of 43.03sec.
"I thought I would never see something like this again. I've been proven wrong," said the man from Grenada.
James, whose career was nearly ended by the auto-immune disorder Graves disease, said he had not run his last race yet.
Asked if he would bid to regain his title in Los Angeles in 2028, he replied: "That's the plan."
