"I'm speechless, really proud of the boys", Fiji captain Jerry Tuwai said.
Willy Ambaka gave Kenya a flawless start scoring under the post with Samuel Oliech getting the extras.
Fiji became the first team to notch two tournament titles this season, leapfrogging New Zealand to move from third to second in the series standings behind South Africa. Fiji grabbed the kickoff for its first possession of the match and Josua Vakurunabili dashed from halfway for a try that leveled the scores.
Fiji had it well in hand when Ambaka went flying down the left wing apparently set to give Kenya a final try only for Tuwai to wrap him up.
Kenya hit the lead again with a try to Samuel Oliech, who fended one defender and side-stepped another.
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Nasilasila also featured in the lead-up to the next try, kicking into open space for Alasi Sovita Naduva, who kicked the ball on and claimed a helpful bounce to score.
Kenya found themselves at the back foot when Perry Baker scored two quick tries to give USA, who has just won USA Sevens, a 14-0 lead.
The win capped a strong day for the Australians, who for the first time under Friend took the field with the same squad as the Las Vegas sevens last week.
Kenya had reached the semis with a 12-0 quarter-final win over England, their first over that side since 2011. Fiji beat Argentina 43-7 and South Africa beat Australia 24-19.
Australia play the South Africa's Blitzboks in the Cup quarter final at 5.08am AEDT on Monday.
The series now heads to Hong Kong for the seventh round April 6-8.