America’s women fell in the semifinals of their own Rugby World Cup Sevens, losing an entertaining game to New Zealand at AT&T Park in San Francisco, 26-21, after leading 14-12 at halftime. The men followed them out of the competition, losing their quarter-final to England 24-19 in sudden-death overtime.

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In the women’s event New Zealand went on to face France, surprise conquerors of the world series champions, Australia, in the final on Saturday evening. New Zealand won that game at a canter, 29-0, to be crowned World Cup champions.

The USA and Australia met before that, in the bronze medal playoff. The Eagles wing Naya Tapper scored two tries – reaching seven in the tournament – but the Australians ran out 24-14 winners.

Before meeting the US in the last four the Black Ferns had not conceded a point. They duly went ahead with a slashing try from Michaela Blyde, who ended the tournament the leading scorer with nine. Two tries by Tapper turned the scoreboard around, the second involving a neat step past Portia Woodman, one of the leading players in the world game.

As American errors and infringements increased, Ruby Tui, Gayle Broughton and Woodman scored the next three tries, Tui and Broughton from long range, securing New Zealand’s passage to the final. The USA fly-half Lauren Doyle got up from a tackle for a smart try that closed the gap to five as the clock ticked to zero.

In the other semifinal, Australia led France 12-0 at halftime, then conceded three tries, the last by Anne-Cecile Ciofani, who scooted around Emma Tonegato on the final play. Chloe Pelle and Fanny Horta had earlier lifted France back into the game.

In the first half, Australia’s Evania Pelite scored a fine solo try to take her tournament tally to five and Ellia Green scored the second after Marjorie Mayans had been shown a yellow card for a deliberate knockdown.

Facebook Twitter Pinterest Martin Iosefo of the United States looks to evade a tackle against England. Photograph: Lachlan Cunningham/World Rugby via Getty Images

The Australian men’s team were also upset by France, in the first round on Friday, leaving them to play for minor placings.

In the men’s quarter-finals on Saturday, South Africa crushed Scotland 36-5 and Fiji strolled past Argentina 43-7. New Zealand then had a narrow in over the French, 12-7, before the USA and England played a thriller.

Captain Madison Hughes put the Eagles ahead after a pass by Maka Unufe, before two England tries made it 12-7 at the half, both by Dan Norton, the second a video referee call. Ollie Lindsay-Hague put England 19-7 up straight from the kickoff for the second seven-minute half before Folau Niua and world player of the year Perry Baker hauled the USA back to 19-19. The decisive try for England came from Phil Burgess, after a kick by captain Tom Mitchell.

The USA will now face Scotland in a placings game on Sunday, the best they can finish now fifth. England will play South Africa in one semifinal while New Zealand and Fiji play the other.