But finishing runner-up was enough to enable the U.S. team to take overall lead in the World Series, one point ahead of New Zealand, the defending champions in Cape Town, whom they beat 31-12 in the semi-finals.
After battling through the semifinals, Fiji and the United States meet for rugby sevens supremacy in the final of the World Rugby Sevens Series in Cape Town, South Africa.
The Fiji men's sevens team have vanquished a couple of demons en-route to winning the latest round of the World Series in Cape Town.
Ethan Waddleton opened the scoring with a converted try for a 7-0 lead, but Kenya responded with captain Edend Agero converting Cyprian Kuto's try to make it 7-7.
Andrew Knewstubb and debutant Taylor Haugh notched New Zealand's only tries with the game already beyond them in the second half.
Sevuloni Mocenacagi scored off Perry Baker's error after he gave up possession when he broke through two half-hearted tackles.
Ben Pinkelman scored two consolations for the USA, either side of Nasoko's second and Fiji's fifth try, a classic from deep by the Pacific Islanders.
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Fiji and England are respectively third and fourth.
"We were disappointed last week that we didn't manage to perform to the levels that we've done this week", he said.
"We'll rest, recover and make sure we're prepared for what day two throws at us".
Needing a win, New Zealand trailed 21-14 with time nearly up but Sione Molia scored his second try in the last minute and Andrew Knewstubb hurriedly kicked a conversion with just a second on the clock to level - and force the game to restart.
Kenya Sevens will be eyeing their first main Cup quarterfinal appearance when they play series champions South Africa, France and Scotland at the Hamiltion Sevens on January 26-27, next year in New Zealand. Fiji had beaten hosts South Africa in the semi-final.
England secured fifth place with a 14-7 win over Spain.
New Zealand won the rugby sevens season opener in Dubai, beating the USA in the final.