It’s been a while. With noticeable problems, they stumbled in the 2021 Olympic semifinals and crashed out of the 2023 World Cup in the round of 16 — the earliest exit in program history.

But here they were in this Mediterranean port city, buzzing for more goals and repelling almost every insurgency en route to three consecutive victories by a 9-2 aggregate score. Two formidable foes — Germany on Sunday and Australia on Wednesday — were not much of a match following a breezy opener against Zambia.

“We really used each game to grow and add different layers to our game, but everyone knows it’s now knockout rounds,” left back Crystal Dunn said. “It’s almost like a completely different tournament.”

Washington Spirit star Trinity Rodman scored late in the first half and substitute Korbin Albert added a remarkable goal in the 77th minute before Alanna Kennedy scored in stoppage time for the Matildas (1-2-0).

On Saturday at Parc des Princes in Paris, the United States will face Japan, which finished second behind world champion Spain in Group C with a 2-1-0 record. The U.S. men will also visit Paris for a quarterfinal, Friday against Morocco.

With a quarterfinal slot already assured, the U.S. women entered Wednesday with a chance to win the group and maintain their positive rhythm. To Coach Emma Hayes, though, there was concern about not finishing the job.

“I said to the girls before the game, ‘This is a banana-skin game,’” the British-born coach said. “They said, ‘What’s that mean?’ They said, ‘It’s called a trap in America.’ I said, ‘Okay, this is a trap game.’”

Hayes explained: “We had to work through the interferences. Whether that’s, ‘Oh, we are going to Paris. Oh, we’ve got to pack. Oh, we’re already through [to the next round].’ This is the game where your conscious brain has to speak to your unconscious brain. And when your unconscious brain starts going, ‘It’s hot. I’m tired. I want to sit down. I want to drink. Can I do this?’ You have to go to the front of your head and say, ‘Next action, next action, next action.’ I thought we were relentless with that. I thought we were in complete control of the game and maybe too careless in the end.”

As the first half wore on, the Americans turned up the heat. Australia’s Mackenzie Arnold pushed Lindsey Horan’s close-range header off the underside of the crossbar and swatted Rodman’s threat.

The breakthrough came on the ensuing corner kick in the 43rd minute, though it took several minutes to confirm it.

Rose Lavelle served the set piece. Australia won the header, but the ball drifted to Sophia Smith on the back side for a downward header through a mass of bodies. It took two bounces before dropping in front of Rodman inside the six-yard box for a quick stab.

Referee François Letexier waited for the video replay crew to rule out any issues. U.S. midfielder Sam Coffey had been in an offside position on Smith’s header, but did she interfere with the play?

A communication issue between Letexier and the video replay officials delayed the ruling. Letexier finally signaled the goal was good. But wait! Another delay. Letexier finally checked the monitor and allowed the goal.

“In your head, you just stay at 0-0,” said Rodman, who also scored in the opener. “You can’t get too excited. … We were like, ‘No matter what happens, we’re in a good spot and we’ll get one even if they call it back.’”

The Americans controlled the second half and expanded the lead when Albert, a 20-year-old midfielder employed by Paris Saint-Germain, smashed a 25-yard shot into the upper corner for her first international goal.

“I actually closed my eyes” while the ball was in flight, she said, “and then I opened them and I was like, ‘Oh my God.’”

Albert’s teammates rushed to embrace her — a notable moment after Albert received criticism this spring, including from current and former U.S. players, for social media activity that supported anti-LGBTQ+ content, among other things.

“We all know she’s been through a lot with her actions and she’s someone who is truly sorry for what she’s done,” Hayes said of Albert, who apologized in March. “She’s a really inclusive person and she’s really thoughtful and kind, and she has had to do a fair bit of growing up.”

Albert said, “It’s tough love sometimes [from Hayes], and it’s really nice just to have her here and teaching me and guiding me in every way — personally and on the soccer field.”

After Albert’s goal, Smith’s deflected shot hit both posts but didn’t cross the line. Kennedy then answered, creating some late anxiety for the U.S. team.

“We knew this was going to be a process and we knew we wanted to focus on the task at hand,” Horan said. “We keep moving forward.”

Notes: Emily Sonnett replaced center back Tierna Davidson, who was sidelined after a knee-on-knee collision against Germany. … Coffey will miss the quarterfinal after receiving her second yellow card of the tournament. … Forward Jaedyn Shaw (leg) was unavailable for the third consecutive match. … Dunn left the match at halftime as part of Hayes’s plan to manage her minutes. … Washington Spirit rookie standout Croix Bethune made her Olympic debut late in the match.