The speedy Oyoo pulled Kenya even, accelerating past Canada captain John Moonlight and scoring under the posts with less than a minute remaining.
Earlier in Pool B Canada beat Kenya 17-14. Samoa ran the ball at the Australian line with aggression and countered with a quick try of their own to take the lead 5-7. Cecil Afrika's try, when he ghosted through a gap with barely a New Zealand hand laid on him, was especially disappointing.
Earlier in the day, they edged New Zealand 21-19 in the Cup quarters.
The Canadian men are 2-43-0 all-time against Fiji and have been outsccored 1,394-437.
Spain secured their spot in next season's World Rugby Sevens Series after beating Germany 12-7 in the final of the qualifying competition.
On New Zealand's side of the draw, the US face England, while the Australia meet Argentina and 16-time Hong Kong champions Fiji face Canada.
The Pacific Islanders were facing the possibility of failing to make it out of the preliminary stage after being held to a 17-17 draw with Wales but ended up finishing top of Pool C after a dramatic last-gasp win over New Zealand.
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I think for players, going to the Olympics is a privilege. "Obviously, they wanted something more, and we still do not know what". He was lucky enough to play for Canada in 2014, with a more prominent role likely waiting for him in 2018.
Mike Friday's side produced a dominant performance against Argentina in their final pool match, with the returning Mike Teo showing his class from the recent Americas Rugby Championship by bagging two tries in his side's five-try, 33-5 win.
"What's important is that we don't take South Korea lightly".
England lost 27-7 to US in the quarter-finals earlier on Sunday, and their misery was compounded when two Joe Ravouvou tries inspired New Zealand to victory.
"When you look back at your career as a coach or as a player, you look back on moments that perhaps didn't go so right", said Baber.
World series leaders South Africa defeated France 17-10 in Pool B, Argentina beat Scotland 22-14 in Pool D, and the United States beat Russian Federation 14-7 in Pool D.
"I think that's the biggest compliment people can say about Perry". Cautious play from both sides would have seen the two teams share spoils for the second time out of 26 times they have met.
"They showed a lot of belief and composure to beat a good United States of America team to finish third", Friend said.
