The United States women’s national team have won a record-extending fifth Olympic gold medal, and their first since 2012. A Mallory Swanson goal broke open a tightly wound final with Brazil in the 58th minute on a sun-splashed afternoon in south-west Paris.

Barely one year after they were held to four goals in as many games in a dismal World Cup that gave rise to questions over whether they had permanently ceded their status as women’s football’s gold standard, the Americans are back on top under new coach Emma Hayes, who is the toast of the US soccer establishment after just nine games on the job in which her team have yet to trail.

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“I’m very emotional. It’s been a dream of mine to be in this position,” Hayes said after the match. “I have to thank my dad because he’s the one who pushed me to this point to be able to come and coach an unbelievable group of players that have received me so well and taken on board everything I have asked. They are tremendous people and players and role models. Yeah, I love them.”

It wasn’t always comfortable for the Americans, who went off as favorites on Saturday but were the worse team for nearly an hour after requiring extra-time to progress through the quarter-final and semi-final stages. But they depart the French capital as deserving Olympic champions behind the stunningly rejuvenated attack of Swanson, Trinity Rodman and Sophia Smith – the front line known as Triple Espresso – and a back four marshaled by center-back Naomi Girma, the lone bright spot of last summer’s World Cup washout who affirmed her status as one of the world’s best center-backs at 24 years old.

Underdogs on merit after barely scraping through the group stage as one of two third-placed teams, the Seleção flew out at the start of the game and immediately dispelled concerns they might sit in a low block. They should have gone ahead in the second minute when Ludmila had an attempt from 10 yards, only to send her shot into the arms of Alyssa Naeher. A brief spell of US possession resulted in a series of corner kicks but it wasn’t long before Ludmila was at it again. The Chicago Red Stars forward appeared to have finished beautifully from an acute angle at the quarter-hour mark only to have the goal ruled offside. Then she just missed connecting with a long cross from Gabi Portilho for a third near-miss in the first 18 minutes.

Playing in front of a rowdy, well-lubricated crowd that broke into warring chants of “U-S-A!” and “Bra-zil!” every few minutes, the US were careless in possession while their full-backs were overrun by a dogged Seleção attack. Brazil’s attacking persistence appeared to be draining a US team already taxed by the condensed Olympic schedule and Hayes’ reluctance to go to her bench. The breakthrough came from nothing in the 58th minute when Korbin Albert, Hayes’ one change from Tuesday’s semi-final win over Germany, threaded a perfectly weighted through ball to Swanson, who coolly slotted a right-footed shot past Lorena, marking her 100th international appearance in style. Swanson’s fourth goal of the Olympics was the latest coup of a partnership with Rodman and Smith, who finished with 10 of the team’s 12 goals during their run to gold.

That was the sign for Brazil manager Arthur Elias to bring on Marta but her introduction did nothing to slow down the emboldened Americans, whose chances were coming in quicker succession. Ten days after her international career appeared doomed to end with the ignominy of a red card, the six-time Fifa women’s player of the year did everything in her power to will Brazil to a first major championship in a half-hour of action.

What might have been Brazil’s final opportunity came in the 88th minute after Marta’s free kick from a dangerous area curled just over the woodwork. But Naeher was called into action on one last occasion during an agonizing 10-minute stretch of injury time, capping a sensational tournament with an acrobatic save of an Adriana header. The save preserved Naeher’s fourth clean sheet of the competition including the entirety of the knockout stage. By then celebrations among the US fans were kicking off in the stands.

Three hundred and seventy-one days after crashing out of the World Cup on penalties after Megan Rapinoe skyed her attempt over the crossbar, the US have capped a dramatic overhaul in sensational fashion. They celebrated in a jumping mass while Rapinoe pumped her fist from the stands.