During the entertaining 45-minute, four-goal match, Sophia Smith struggled through an ankle injury she suffered in the season opener and scored twice more before halftime to give the Americans a 4-1 win and advance to the quarterfinals.

A win or draw for the Americans (2-0-0) against Australia (1-1-0) in Marseille on Wednesday would secure top spot in Group B and a trip to Paris for a quarterfinal on Saturday. Germany (1-1-0) will face Zambia (0-2-0) in the other match. Two teams receive automatic berths and one could advance to third place.

“I really enjoyed the game,” U.S. coach Emma Hayes said. “The pace, a high-level game, a high-level opponent, a high level of tactics, a high level of technical execution on our part — that was a mature performance. … They’re a top team, but we were devastating when we needed to be.”

The front line of Smith, Mallory Swanson and Trinity Rodman has been particularly devastating. Through two games, they have combined for six goals and three assists. Smith’s backup, Lynn Williams, also scored on Sunday.

Hayes called them “dynamic as hell, really fun to watch. And most importantly, they enjoyed it.”

Smith opened the scoring in the 10th minute. After Germany drew level, Swanson scored her third goal in two games and Smith struck again just before half-time. Williams added insurance in the 89th minute.

“I feel like we’ve really gelled together really well and quickly,” Smith said. “This is only 70 percent of what we can do. The more games we play together, the more we play against each other and learn each other’s tendencies. It’s so much fun playing with them.”

The feat came against a German team ranked fourth, one spot above the United States, which is in its lowest position since FIFA began ranking women’s teams in 2003.

Three days after squandering countless chances in a 3-0 win over Zambia — continuing a three-game streak of missed chances — the Americans were back on track.

Smith was called into action after leaving the opener with a first-half ankle injury, and capped an artistic team possession with some great build-up and execution. Emily Fox, Rodman and Rose Lavelle worked the ball down the right. Lavelle’s pass freed Rodman who blazed past her marker. As Rodman crossed, Swanson’s run at the near post provided a distraction. At the back, Smith met the ball for a simple one-timer.

“I’m glad I made the decision to play (against Zambia),” Smith said, “because I felt good today.”

Germany responded in the 22nd minute when right back Giulia Gwinn was given the time and space to perfectly place a shot from 23 yards, past the reach of goalkeeper Alyssa Naeher.

The Americans needed just four minutes to regain the lead. Smith won the ball outside the penalty area and fired upward. Ann-Katrin Berger made a two-handed save but failed to hold the ball or push it out of danger. Swanson was there first and slotted home the rebound.

In the 44th minute, Smith scored again. Initially missing a one-timer with her left foot, she held on, slid the ball across the top of the box and tapped in a right-footed shot that deflected off defender Felicitas Rauch, flew over Berger, hit the right post and spun over the line.

“Soph does Soph things — plain and simple,” Swanson said. “That first goal felt really good as a team … something that went straight from the practice field to our game. That was super special. The second shot, I’ve seen her do that a million times in (the NWSL). When she gets in that position, it goes in.”

Early in the second half, Germany pushed hard. Jule Brand hit the right post and Naeher blocked Sjoeke Nüsken in the penalty area.

“There were times when we had to weather a storm, especially in the second half,” Williams said. “The great thing is that nobody looks scared in those moments.”

Hayes was unhappy with the misses, saying: “There are still things that annoy me about us but I have to fix that. We could have controlled more. We let Germany back into the game partly because of our decision-making.”

The U.S. team regained its composure. Smith left to a standing ovation in the 85th minute — four minutes before Swanson set up Williams on the left side of the penalty area for a shot into the far corner past Berger, her Gotham FC teammate.

“It’s only three points,” Hayes said. “We’ve got to build momentum. First of all, can you imagine the adrenaline that comes after games like this? That’s probably my biggest worry right now. You get so high, the comedown is like any hangover.”

Remark: Central defender Tierna Davidson will undergo tests in the coming days after being taken out of the game late in the first half following a knee-to-knee collision.