Collins Injera moved within two tries of Argentina's Santiago Gomez Cora leading mark of 230 in the all-time scoring charts with a double in the upset victory at the National Stadium to secure Kenya's first title in 17 years.
Kenya had only scraped through to the knockout stages after beating Russia, drawing with Scotland and losing to South Africa, but a series of upsets on day one handed them a favourable draw.
The Africans beat France 28-7 in the quarter-finals and Argentina 15-12 in the semis on Sunday before taking out the Fijians.
Kenya 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.
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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.
Rugby Sevens will feature in the Olympics for the first time at this year's Games in Rio de Janeiro.
(Reporting by Patrick Johnston, editing by Ed Osmond)
