Trinity Rodman's moment of magic in extra time was enough for the United States to see off Japan and progress to the Olympic semi-finals.

The two sides laboured in the first half, with Emma Hayes' team enjoying plenty of possession but struggling to create any meaningful chances at the Parc des Princes.

The USA improved after the break and their first decent opportunity arrived in the 63rd minute when Mallory Swanson exchanged a one-two before curling an effort just wide.

Rodman's influence grew as the game wore on, but it was Sophia Smith who had the best chance prior to the USA's winner, only for the 23-year-old to take too many touches when through on goal, allowing Ayaka Yamashita to close down the angle.

But as penalties approached, Rodman stepped up in the second minute of stoppage time at the end of the first half of the additional 30 minutes, collecting Crystal Dunn’s pass before cutting inside and curling in an unstoppable shot.

Japan substitute Riko Ueki almost equalised from close range, but the USA were able to clear their lines and hold firm to tee up a semi-final against either Canada or Germany.

Data debrief: USA fail to convert possession into opportunities

Despite neither side creating much in the way of chances with the USA mustering an expected goals (xG) of 0.68 to Japan's 0.53, the Americans dominated the ball for large swathes of the match.

They had 71.3% possession, had more than double the passes and final third entries of Japan with 1,026 to 403 and 89 to 44 respectively.

But it ultimately took a moment of brilliance from Rodman to settle the contest. At 22 years and 75 days old, she is the youngest player to score an extra-time goal for the USWNT since Heather O'Reilly at the 2004 Olympics in Athens.