Like the arduous quarter-final win over Japan, this edgy victory was a reality check after the exuberant thrashings the US have doled out in the sunrise phase of the Emma Hayes era.

But a win will do, any which way – especially when it means the USWNT are in the Olympic final. A year to the day since one of their lowest ebbs, the loss on penalties to Sweden in the first knockout stage of the 2023 World Cup, a hard-fought and sometimes hard to watch 1-0 extra-time victory over Germany sent the US into Saturday’s final against Brazil, ensuring the Americans at least a silver medal.

The team is yet to recapture the imperious brilliance that was the hallmark of American sides of yesteryear; perhaps it never will, given the dramatic improvement of other nations. But in reaching the Olympic final the US are back on a familiar stage after the uncertainty and insecurity of the past couple of years under the previous head coach, Vlatko Andonovski, as a group of exceptional veterans endured a slow fade.

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After winning four Olympic golds and a silver from 1996 to 2012, the US lost in the quarter-finals in Rio then had to settle for bronze in Japan three years ago. Now they have the chance to play for another championship, though given the pattern of play in the semi-final it was tempting to wonder if the 4-1 win over Germany in the group stage nine days earlier was the worst thing that could have happened to the US.

That scoreline did not tell the whole story, since the sides were more or less even in terms of attempts on goal. But the embarrassment evidently prompted Germany to revise and redouble their efforts to establish a tactical bulwark against the usually effervescent attacking trio of Sophia Smith, Mallory Swanson and Trinity Rodman, who provided eight of the US’s 10 goals coming into this match but were only sporadic threats on Tuesday.

Rodman had scored the extra-time winner as the US overcame Japan 1-0 in the quarter-finals, finally solving a stubborn low defensive block with a moment of individual inspiration. Up to that point, goals were not hard to come by, with the US beating Zambia 3-0 and Australia 2-1 in the group stage as well as putting four past Germany.

As against Japan, a fine extra-time goal was enough to overcome determined and well-drilled opponents and continue Hayes’ run of stellar results. The 47-year-old Londoner now has eight wins and a draw in her opening nine games with the US, the first of which, a 4-0 victory over South Korea, was only two months ago. She’s not wasting any time as she seeks to return the US to global dominance and build a young, irrepressible lineup.

The celebrations at the final whistle were understandably exuberant, a release of emotion after a tense night. There was one of those rare first periods when so little happens that the referee overlooks the delays caused by fouls and blows the half-time whistle without adding any stoppage time; a merciful act in this case.

The atmosphere was muted, with the 60,000-capacity home of Olympique Lyonnais far from full, and in any case there was little to rouse the modest crowd, the “U-S-A!” chants assuming a tunnel-like echoing timbre in the vast arena. The contest devolved into a dour midfield battle that better suited the Germans, who recovered from a shaky start to successfully smother American attacks while mounting the occasional offensive foray of their own.

An early sighter from Rose Lavelle after three minutes was handled easily by the resilient goalkeeper Ann-Katrin Berger (of Gotham FC and formerly of Hayes’s Chelsea). But the chance, a menacing run from Rodman and the amount of space generally available to the US in the final third looked like bad omens for Germany.

Yet the underdogs had the best opportunity of the first half, with US goalkeeper Alyssa Naeher forced into something close to full stretch to push away a low shot from Jule Brand in the 24th minute. The US led 3-1 at half-time when the teams met in the group stage nine days earlier; on this occasion they were level at the break.

As the second half got under way, Naomi Girma was in commanding form alongside Emily Sonnett, who came on at the break for Tierna Davidson. That the American center backs were increasingly relevant underlined Germany’s growing confidence and threat, while the US offered too much patience and too little pace. US possession was often spent passing the ball sideways, failing to provide territorial progression while giving Germany ample time to settle into their defensive shape.

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Girma took matters into her own feet soon after the hour, crusading into midfield and brilliantly finding Swanson, who rounded the goalkeeper but sent her shot wide rather than square the ball to a teammate for a simple finish, though there was a suspicion of offside.

The US turned the screw in the final minutes of the second half but Germany held firm to send the contest into extra time. Having ousted the defending champions, Canada, on penalties in the quarter-finals, they would hardly have been averse to a shoot-out.

The dynamic Smith, though, had other ideas. Neatly fed by Swanson five minutes into extra-time, she beat Feli Rauch and the onrushing Berger to the pass and slid the ball into the net. Rather than whirring off in celebration, Smith dropped to the ground in exhaustion, saying post-match that she was too tired to run and so opted to have her teammates come to her.

Broadcast microphones picked up Hayes directing the team from the sideline, urging the players to “Hang in there”. And so they did, despite late German pressure, with Naeher called into acrobatic action again with a terrific late save, while Smith might have had another couple of goals as Germany left gaps at the back.

Hayes, as everyone knows, is a winner; the only question now is the colour of the medal. Asked post-game whether she wanted to face Spain in the final, Hayes said: “I don’t care. I want a drink.”

As it transpired, Brazil stunned the World Cup holders 4-2 later on Tuesday. The most recent meeting between Saturday’s finalists came in San Diego in March, a 1-0 US win in the Concacaf W Gold Cup final. Hayes will take nothing for granted against opponents who ground out an impressive quarter-final victory over the host nation. But in Paris it’s never hard to find a bottle of champagne on ice.