The U.S. win over Brazil also sent the Czechs through to the last eight despite their 84-77 defeat by Greece but they now face a daunting clash with the Australians, who stretched their perfect record to five successive wins.
Those two quarter-finals will be played on Wednesday while Serbia take on Argentina and Spain will start as strong favourites against Poland in Tuesday's action.
Monday's results also mean that the United States and Argentina qualified for next year's Olympic Games in Japan as the two top-ranked teams from the Americas in the 32-nation tournament in China.
USA men lose to Australia in second shock defeat
They joined Australia, who earlier booked their berth by advancing into the second group stage as Oceania's best-placed team with New Zealand dropping into the 17-32nd place playoffs.
The top two teams from Europe will also qualify as well as one each from Africa and Asia.
Brazil held their own against the more athletic Americans in the opening half and were level 23-23 at the end of the first quarter before the champions engineered a 43-38 halftime lead.
A barrage of fast breaks coupled by Marcus Smart's audacious three-pointer on the buzzer gave the U.S. a 68-57 lead at the end of the third quarter and the Brazilians ran out of steam in the final 10 minutes.
Guard Kemba Walker and centre Myles Turner netted 16 points each for the U.S., who dished out 21 assists to Brazil's 12 and racked up 11 steals.
Australia, who reached the 2016 Olympics last four, appear set to at least emulate the achievement after they garnished another impressive performance with a dramatic win in the last few seconds of a rip-roaring contest against the French.
The lead changed hands throughout with both teams trigger-happy from three-point range before Matthew Dellavedova and Mitch Creek sank a free throw each in the final few seconds to seal Australia's win as France threw away their last possession.
San Antonio Spurs playmaker Patty Mills shone with 30 points for Australia, Joe Ingles added 23 and Aaron Baynes chipped in with 21 as the Boomers' ironclad backbone carried them again.
Orlando Magic guard Evan Fournier nailed a game-high 31 points for France and Nando De Colo added 26 but the French will rue spilling a 70-61 lead in the third quarter when they appeared to be in the driving seat.
Greece needed to beat the Czechs by at least 12 points in the day's opening fixture and hope that the U.S. beat Brazil in order to advance, but came up short although they were 65-53 ahead early in the fourth quarter.
Their top performer Giannis Antetokounmpo, last season's most valuable player in the NBA, fouled out shortly afterwards and the Czechs managed to slash the deficit thanks to some lethal long-range shooting.
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