Paris - Megan Rapinoe is already looking forward to the United States's mouth-watering quarter-final date with Women's World Cup hosts France after her two penalties squeezed her side past resilient Spain 2-1 on Monday.

The reigning world champions will face the French in Paris on Friday in a match that could well decide the destiny of the tournament after Rapinoe struck from the spot in the seventh and 75th minutes to decide a last-16 contest played in sweltering conditions in Reims, and Rapinoe hopes it becomes the big moment for women's football.

"I hope it's wild and crazy and the fans are crazy and that there's tonnes of media around it and it's just a big spectacle," Rapinoe said of Friday's match.

"I think it's going to be incredible for the women's game. You have two heavy hitters meeting in the knockout rounds and this is everything you want."

The Americans will need to improve after being pushed all the way by Spain, and the small portion of the crowd not supporting the USA reacted furiously after the winning penalty was given for what looked a very slight touch on Rose Lavelle from Virginia Torrecilla.

"I didn't touch her... they blew for that penalty because it was the United States," a distraught Torrecilla told reporters afterwards.

"I am sure they gave that penalty because it was the USA, the best team in the world. If it had been in the other area it would not have been punished."

However Lavelle insisted she was brought down for the winning penalty, despite the boos that rained down on Rapinoe as she fired home.

"I got a kick on the shins! A foul's a foul and I'm glad she (referee Katalin Kulcsar) called it," she said.

Rapinoe's winner decided a keenly-contested match in which Spain caused the USA serious problems at the back, which could give France hope of sending Jill Ellis' superstar team home.

"Spain are a very good team and if you look at the games they have played this year like I have they have dominated most of their opponents. In fact all of their opponents," said coach Ellis.

"It's about how you look at things. If your glass is half empty you might look at it differently but I'm half full so I'm like 'holy shit that was awesome'."

The USA thought they were ready for an easy afternoon when Tobin Heath was brought down by Maria Leon after brilliantly collecting Abby Dahlkemper's searching long pass.

Rapinoe lashed home the subsequent spot-kick to send the overwhelmingly American crowd wild, but Spain stunned them back into silence shortly afterwards.

Goalkeeper Alyssa Naeher played a sloppy pass to a dozing Becky Sauerbrunn, who let Lucia Garcia nip the ball from her feet before feeding Hermoso who arced a super strike over Naeher.

Spain held their own against a team most observers expect to lift the trophy in Lyon come July 7, but were undone with 15 minutes left when referee Kulcsar whistled for another spot-kick.

The penalty was confirmed after a VAR check and Rapinoe smashed the ball into the same corner to give the USA the tightest of wins and line up the French in possibly the most highly-anticipated match in the history of women's football.

"From the bench we can't see," said Spain coach Jorge Vilda. "The referees have analysed the pictures before making the decisions. We still accept the refereeing decisions so there is nothing else to say."