Kenya have shocked Australia but then lost to Japan to afford the defending World Rugby Sevens champions fortunate passage to the quarter-finals in Los Angeles.
John Manenti's side lost two of three games on the opening day of the USA series leg marred by heavy rain and storms that forced a lengthy stoppage in play.
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A 12-7 loss in their opener to the plucky African outfit was almost a costly one for an Australian side that's slipped to eighth in the series standings and outside the automatic qualification zone for the Paris 2024 Olympics.
A must-win clash with Fiji loomed but when World Series battlers Japan - beaten 50-0 by Fiji and 24-10 by Australia early in the day - upset Kenya 7-5 it gave the men in gold some room for error.
They initially looked like they didn't need it, up 12-5 against Fiji in driving rain at halftime of their final pool game thanks to Maurice Longbottom and Nathan Lawson tries.
But second-half turnovers in a line-out, from a quick tap and then a scrum, combined to squander that lead as Pilipo Bukayaro scored with 20 seconds to play as Fiji won 15-12.
Australia still snuck through in second place, thanks to Japan's upset win in the preceding game.
They'll meet ninth-ranked Ireland in Monday's (AEDT) quarter-final, chasing a podium finish for the first time since their Hong Kong gold kick-started the season five legs ago.
Sunday's other quarter-finals will see Great Britain take on New Zealand while Fiji will face South Africa.
Samoa will play Argentina in the other quarter-final.
Samoa topped Pool A with maximum points after a hard-fought 14-7 win over New Zealand in their group decider.