LYON, France -- It took extra work yet again, but the U.S. women's national team will play for the gold medal after outlasting a resilient Germany, 1-0, in a semifinal here on Tuesday night.

Sophia Smith burst into the spotlight just in time for the Americans, scoring the game-winner in the 96th minute to send the U.S. to the ultimate match of this Olympic tournament on Saturday in Paris. They will face either Brazil or Spain, who were to play later Tuesday in the other semifinal.

Smith's goal came at the end of a sluggish, stilted match played in steamy conditions, and if that recipe for U.S. success sounds familiar, that's because it is; just three days ago in the quarterfinals, it was one of Smith's frontline partners, Trinity Rodman, who scored in extra-time to break a scoreless tie and send the U.S. through over Japan.

Rodman's strike was a rocket, a blast from distance that rippled the upper corner of the goal. This one was more precise, as Mallory Swanson played a ball in behind and Smith capitalized on a moment of hesitation from Germany's goalkeeper, Ann-Katrin Berger, and defender Felicitas Rauch.

With the ball rolling between the two Germans, Smith lunged in and sent the ball over Berger and into the net. She then fell on her back -- some combination, almost surely, of exhausted and relieved -- as her teammates tumbled beside her.

After playing the quarterfinal in front of a packed crowd at the Parc des Princes in Paris, the U.S. performed on a significantly less-raucous stage here. The stadium here holds about 60,000 fans but was only a quarter-full for this match, making it easy for nearly everyone in the building to hear Hayes shouting at her players from the sideline.

The game began at a languid pace, too, likely due both to the intense heat -- temperatures were near 90 degrees Fahrenheit -- as well as a bit of hesitancy from the Germans, who were forced to make two unexpected changes to their preferred lineup.

Alexandra Popp, the team's captain, was a late scratch due to illness while dynamic forward Lea Schüller was also left out with inflammation in her left knee. Given that Germany had both those players available in the group stage match with the U.S. and still lost, 4-1, it wasn't an ideal development.

As expected, the U.S. started well. With Tierna Davidson back from a knee injury and Sam Coffey returning from suspension, the U.S. was able to use its Match 1 alignment and went immediately into attack. Berger had three saves inside the first seven minutes, though none of the shots -- from Davidson, Rose Lavelle and Smith -- were particularly fierce.

In truth, the best early chance was Germany's. Jule Brand whirled and fired from close range and, if not for a strong hand from Alyssa Naeher, the Germans would have had a 24th minute lead that was (mostly) against the run of play.

The U.S. continued to probe, often playing down the left, where Crystal Dunn was incredibly active, but were just as often stymied by Germany's defensive aggression. The referee's whistle was a constant; Nicole Anyomi sent Emily Fox flying with a shoulder barge that was the most notable moment of physicality, while Germany finished the half with 11 fouls to the Americans' 4.

Hayes looked to inject some energy on the hour, bringing on Lynn Williams in place of Lavelle with Swanson dropping a bit deeper into the midfield -- a tweak that proved critical. Naomi Girma, who was the best U.S. player throughout in center defense, responded within minutes by playing Swanson in behind the German backline only to see Swanson hit the side-netting as the assistant referee raised her flag.

Smith had an even better chance about five minutes from time -- she even got the ball in the back of the net -- though her smart finish after running in behind was only possible because she, too, was well offside.

Frustrated as they were, that combination was what the U.S. needed. Six minutes into extra time, Swanson tried again, and this time Smith held her run perfectly before surging forward to send the U.S. back to Paris.