It took Kenya 140 tournaments to break their duck and they are only the second African nation after South Africa to win a World Series leg.
Kenyan president Uhuru Kenyatta said on Twitter: "Join me in congratulating the Kenya Sevens Rugby Team on their remarkable win."
Rugby Sevens will feature for the first time in this summer's Olympics in Rio.
Kenya, who have qualified for the Olympics in the men's and women's event, opened up a 20-0 half-time lead over the favourites with two of their four tries from Collins Injera.
Fiji, coached by former England Sevens coach Ben Ryan, briefly rallied after the break, but Kenya held firm and scored two further tries to seal a convincing win.
Kenya have shot up to seventh in the standings after their 22-point haul in Singapore, with Fiji extending their lead at the top to eight points over South Africa with two rounds remaining in France and England.
South Africa, beaten narrowly by Fiji in the semis, finished third after thrashing Argentina 28-0.
Samoa landed the second tier Plate title after causing another upset in beating New Zealand, Scotland edged United States to land the Bowl and Russia crushed Wales to win the Shield.
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Kenya shocked Fiji 30-7 in the final of the Singapore Rugby Sevens to claim their first World Series title.