Rapinoe's free-kick five minutes into this quarter-final evaded a sea of bodies in the 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 centre, although Wendie Renard pulled a goal back for France to set up a tense finish.
Jill Ellis's team held on and go through to a semi-final against England in Lyon next Tuesday as they seek to retain their crown and win a fourth World Cup in eight editions.
“We didn't have the best night on the ball but the focus defensively, and the willingness and the discipline to do what we did tonight is tremendous,” said the 33-year-old Rapinoe.
“We were ruthless with our chances, so moving on to the next round, that's really all that matters. It's a game that we'll never forget here in Paris.”
France will leave their own tournament with more than a few regrets.
The hosts were the only team to defeat the USA in the two years leading up to the World Cup but they could not repeat the feat here before an expectant crowd.
Coach Corinne Diacre had been set the target of going all the way to the final on home soil, yet 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.
“It's a failure in a footballing sense, we can't hide from that. We are far from fulfilling our objective,” said Diacre.
“I hope we at least won people's hearts tonight and since the start of the tournament.”
The other quarter-finals will be played on Saturday, with the Netherlands meeting Italy in Valenciennes before Germany take on Sweden in Rennes.