Jacobs, who only switched away from long jump in 2018, streaked clear to win in 9.80 seconds, 0.04 clear of American Fred Kerley.
Canada's Andre de Grasse won a second successive Olympic bronze in third.
World champion Christian Coleman and Trayvon Bromell, the world's fastest in 2021, were both absent from the final.
Coleman, banned for whereabouts failures after missing three drugs tests, and Bromell, eliminated in the semi-finals, were joined on the sidelines by the long-retired defending champion Usain Bolt.
Few would have picked Jacobs, who was born in Texas to an American father but moved to his mother's Italian homeland before his first birthday, as the Jamaican great's successor.
Jacobs only broke the 10-second barrier for the first time in May.
But the European indoor 60m champion carried the momentum from his fast start all the way to the line to register a time faster than Bolt's winning mark in Rio.
He was greeted by compatriot Gianmarco Tamberi, who had won a joint high-jump gold just minutes before and wrapped him in the Italian flag and an embrace.
"I don't know, it's a dream, a dream, it is fantastic," said Jacobs.
"Maybe tomorrow I can imagine what they are saying, but today it is incredible."
Second-placed Kerley admitted Jacobs was a new name to him.
"I really didn't know anything about him. It was my first time racing him at the Monaco Diamond League [where Jacobs finished third in 9.99 seconds]," he said. "He did a fantastic job."
Hughes will be left to wonder what might have been in a final stripped of its usual stars and big names.
His clear false start brought back memories of defending champion Linford Christie's disqualification at Atlanta 1996 and denied him a shot of joining the most prestigious honour roll in athletics.
Hughes, who made the same mistake at last month's British Championships, said it was the result of a sudden cramp in his calf.