In Group G, South Africa beat Italy in a 3-2 thriller and Sweden had a comfortable 2-0 victory over Argentina.
Kadidiatou Diani scored a hat-trick in Sydney as fifth ranked France finished top of Group F with seven points. Only needing a draw to qualify, France was stunned in the second minute when Panama captain Marta Cox scored a spectacular goal from a long-range free-kick.
France regrouped superbly with Diani scoring twice as they powered into half-time with an almost unassailable 4-1 lead. Diani completed her hat-trick with a penalty kick shortly after the interval before France took the foot off the pedal.
Panama received consolation goals when Yomira Pinzon scored a penalty and Lineth Cedeno headed home late, but the result was never in doubt. With the draw they needed against Brazil in Melbourne, Jamaica progressed into the round of 16 for the first time.
Playing with trademark defensive might, Jamaica continually frustrated Brazil who struggled to create clear opportunities despite legendary striker Marta Vieira da Silva being recalled into the starting line-up. It was a disappointing exit for Brazil, who finished with three points as a first World Cup title remains elusive.
MARTA’S WORLD CUP LEGACY went beyond her play on the pitch. She was also a next-level leader, as shown in this speech for the ages after Brazil lost to France at WC ’19. “Cry in the beginning so you can smile at the end” one of all-time great footballing lines. �������� pic.twitter.com/UNxHr4iZD7
Earlier, in a dramatic finish in Wellington, Thembi Kgatlana scored the winner in the 92nd minute to eliminate Italy, who finished one point behind second-placed South Africa in Group G. South Africa will play 2019 runner-up Netherlands in the round of 16.
"This is just amazing. I thought they were incredible. We were going to fight for every ball. We're not going to give up and they were absolutely magnificent," South Africa coach Desiree Ellis said.
Arianna Caruso scored both of Italy's goals and appeared to have secured the draw they needed to progress with an equaliser in the 74th minute before Kgatlana's heroics in stoppage time. Italy, ranked 38 spots higher than South Africa, was left in tears by their early exit.
"I don't think I can find the right words in this moment," Caruso said. "I am not happy because we scored two goals and we didn't do anything."
���� ⚽ The South Africa women’s football team has made history for their nation after claiming their first Women's World Cup win with a thrilling 3-2 victory over Italy. Coach Desiree Ellis, a long-standing icon of African women’s football, has led her team into the last 16. pic.twitter.com/PA5lkQ1ceu
Third-ranked Sweden topped the group after a 2-0 victory over Argentina in Hamilton to book a blockbuster round of 16 clash with title holder the United States on Sunday in Melbourne.
"The U.S. are ranked number one. It might be better to play them on Sunday than in the semis or final. From a psychological perspective we know we can beat them. I think the players are convinced they can definitely win on Sunday and I believe that too," said Sweden coach Peter Gerhardsson.
With Sweden's spot already assured, they made nine changes against Argentina but still dominated and hit the scoreboard through a Rebecka Blomqvist header in the 66th minute and a late Elin Rubensson penalty. Sweden joined Japan and England as the only teams to have won all three games so far in the tournament.
The group stages conclude on Thursday when Colombia plays Morocco and Germany faces South Korea to determine Group H placings.