Rapinoe converted either side of Jennifer Hermoso’s equaliser for Spain at Stade Auguste-Delaune.

Victory sets up a last-eight clash with host nation France in Paris on Friday (June 28).

Rapinoe's first goal came in the seventh minute after María Pilar León had brought down Tobin Heath, but Spain were level less than three minutes later when Hermoso fired home after Becky Sauerbrunn had been dispossessed.

The US were awarded another penalty deep into second-half after Rose Lavelle was adjudged to have been fouled by Virginia Torrecilla.

The decision stood after a lengthy review from the Video Assistant Referee (VAR) officials and Rapinoe held her nerve to strike in low from the spot for a second time and secure victory for her side.

Also progressing through to the quarter-finals today were Sweden after they edged Canada 1-0 at Parc des Princes in Paris.

Stina Blackstenius scored the only goal in the 55th minute, clipping the ball over goalkeeper Stephanie Labbé with the game's first shot on target.

Canada had the chance to draw level from a penalty, awarded for a handball by Kosovare Asllani, but Janine Beckie's attempt was superbly saved by Hedvig Lindahl.

There was almost controversy at the end as Australian referee Kate Jacewicz spoke with the VAR team after the final whistle had sounded about a potential handball by Linda Sembrant in the box.

Jacewicz had the option of restarting play, but Sembrant's arm was by her side so the penalty was not given and Swedish celebrations could continue.

Awaiting Sweden in the quarter-finals are Germany with that match scheduled to be held in Rennes on Saturday (June 29).

The FIFA Women's World Cup is due to continue tomorrow with the final two last-16 matches.

Italy face China before The Netherlands go up against Japan.