New Zealand had only two reserves instead of the usual five after a sapping 7-5 win over England in the semi-finals.
Click below to catch the highlights on Saturday at 2 p.m. ET on CBC Sports' Road to the Olympic Games.
On Friday, New Zealand's Black Ferns beat Canada 26-14 in the women's final.
Final: New Zealand 21 (Tone Ng Shiu, Dylan Collier, Ngarohi McGarvey-Black tries; Andrew Knewstubb 2 con, Vilimoni Koroi con) US 5 (Stephen Tomasin try).
England left it to the final play of the bronze final to avenge their day one loss to Australia, this time by the slenderest of margins of 15-14, and claim the medal for the third year in a row.
Half-back Johnstone Olindi scored the first try for Kenya for his first ever in the HSBC World Rugby Sevens Series with veteran Dennis Ombachi crossing over for the second.
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In the rematch, New Zealand took a 7-0 lead, but the US capitalized on a penalty to make it 7-5.
"I'm so pleased with the girls' performances today - the amount of effort and work that everyone put in has been unbelievable", said Brown.
Earlier in the Cup quarter-finals, England kicked day two off with a head-turning 22-5 defeat of the defending Dubai and series champions South Africa. "They ran until they dropped & exceeded all my expectations with some great rugby". Its best finish on the circuit was sixth.
After surviving a Scottish assault on their line, New Zealand then finished off a scintillating attack that started from behind their own posts and Knewstubb was the last man on the end of a brilliant move.
The top four teams secure qualification for the 2020 Olympics, with the next women's event in Sydney in February.
Justin Geduld picked up a knock in the Blitzboks' second match of the Dubai Sevens against Samoa. Failure to do that means having to go to a regional qualifier. The men failed to qualify.
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