Rapinoe's goals sends hosts out and lands USA a spot in the semi-finals

Rapinoe's free-kick five minutes into this quarter-final evaded a sea of bodies in the penalty box on its way into the net to stun the home crowd at the Parc des Princes.

The USA then soaked up pressure before delivering the knockout blow midway through the second half when Rapinoe turned in Tobin Heath's low centre, although Wendie Renard pulled a goal back late on for France to set up a tense finish.

Jill Ellis's team held on and they go through to a semi-final showdown with England in Lyon next Tuesday as they seek to retain their crown and win a fourth World Cup in eight editions.

They once again displayed here how hard they will fight to keep hold of their title, and they have now won their last 10 World Cup matches.

The pink-haired Rapinoe has been crucial on the field in this run, while dominating headlines off it thanks to her spat with President Donald Trump over her refusal to attend any post-tournament reception at the White House.

The 33-year-old had already scored both goals in the 2-1 win over Spain in the last round. Here, she took her tally for the tournament to five goals on the occasion of her 157th cap.

- French regrets -

Meanwhile, France will leave their own tournament with more than a few regrets. 

They were the only team to defeat the USA in the two years leading up to the World Cup and they did not really do themselves justice here before an expectant crowd, at least until it was too late.

Coach Corinne Diacre had been set the target of going all the way to the final on home soil, but that always looked a tall order from the moment the draw was made last December and they were set on a quarter-final collision course with the best team in the world.

Only once before had they even made it to the semi-finals, and for the second World Cup running their adventure ends in the last eight, the same stage at which they went out of the 2016 Olympics and the last three European Championships.

Having started this tournament with a first-half blitz against South Korea in the opening game, Les Bleues never really reached the same heights again.

The country's leading sports daily L'Equipe had called this "the challenge of a lifetime", and in that context conceding the opening goal so early on a sweltering Parisian evening was a disaster.

Alex Morgan drew a foul from Griedge Mbock outside the penalty box to the USA left, and Rapinoe's low delivery somehow went in without taking a touch, passing through the legs of France skipper Amandine Henry en route.

The home side had lots of the ball after that but rarely looked like troubling USA goalkeeper Alyssa Naeher and their supporters grew increasingly frustrated.

Their opponents had not created much either, but they made their intent clear right at the start of the second half as a Samantha Mewis strike drew a fine save from Sarah Bouhaddi, who then did well to keep out Heath's follow-up.

The second goal arrived in the 65th minute, with Morgan and Heath combining down the right before the latter's ball across goal was turned in by Rapinoe.

Heath then had a third goal disallowed for offside but France did not give up and set up a frenzied finale as they reduced the deficit nine minutes from time.

Gaethane Thiney flighted a free-kick from the left into the box and Renard evaded her marker to head home her fourth goal of the tournament. But the USA saw out the victory.