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.
