This was fifth time that the women's 3000 metres steeplechase was contested at the Summer Olympics.
Valerie Constien, Faith Cherotich, Alice Finot and Courtney Wayment were high on the world list.
After the four formed a break a lap into the race, Yavi, on the front of the second group, bridged the small gap to tag onto the back of the pack.
Through the final water jump Chemutai held the inside line and the advantage.
Behind them Alice Finot, running fastest of all of them, picked off Alamyew and a fading Chepkoech, setting her sights on Cherotich.
At first it looked like Chemutai had the advantage, but not known as a fast finisher, Yavi exhibited better sprint form and speed, pulling away for the gold.
Even further back Elizabeth Bird became the #19 performer with a new British Record and Lomi Muleta became #22.