Yavi jumped for joy after crossing the line, having overtaken Chemutai with an explosive final sprint that left the Ugandan who had led most of the race unable to respond.
Chemutai was in tears after Yavi, 24, stole the finish to add the Olympic title to last year's world championship, setting an Olympic record of 8 minutes 52.76 seconds.
"This is like a dream come true. It's something special," Yavi told reporters. "It means a lot to me and also to the country."
Kenyan 20-year-old Faith Cherotich, ranked third in the world, claimed bronze on her Olympic debut.
Kenya's Beatrice Chepkoech took an early lead and was shoulder-to-shoulder with Chemutai but faded in the last lap and ended sixth, while France's Alice Finot celebrated her fourth-place finish in a very fast race.
Chepkoech, 33, holds the world record of 8:44.32 but has never won an Olympic medal in the event.
In Tokyo, it was Chemutai who delivered the upset and took the gold from favourite Chepkoech to become the first Ugandan woman to win an Olympic medal in any sport.
