(CNN) The most anticipated match of this Women's World Cup did not disappoint. In a colossal contest on a summer night in Paris, the US prevailed over host France to move a step closer to successfully defending its title.

Every blockbuster needs a fine storyline and the script for this quarterfinal is one that will stand the test of time because it was Megan Rapinoe -- the USWNT co-captain who had irked US President Donald Trump earlier in the week -- who was the match winner, scoring in each half to secure a hard-fought 2-1 win.

A knockout tie between arguably the two best teams in the world was always going to send a favorite packing. The reason why ticket prices went in the same direction as the temperature in the French capital for a match billed as "Le Grand Match" was because no one could confidently predict how a match between such two strong teams would unfold.

A drilled Rapinoe free kick gave the defending champion the lead in the fifth minute, and the midfielder doubled the advantage after the break by directing a Tobin Heath cross home.

With a team of the US' know-how enjoying a two-goal advantage, the match seemed set for a straightforward conclusion but an 80th-minute Wendie Renard header raised the decibels inside the stadium and sowed some seeds of doubt.

Les Bleues were denied a late penalty appeal against a US side in retreat but, after a pulsating 90 minutes, the experience, composure and ruthlessness of the US proved decisive against an opponent which has never been beyond the last eight of a World Cup.

Rapinoe celebrates scoring her team's first goal against France.

Rapinoe, who had picked a fight with the US President for saying she would not go to the White House if the US were to win the tournament, had said she hoped the match would be a "total sh*tshow circus." It was certainly a spectacle with plenty of talking points, many of which centered around Rapinoe herself, a player who the focus of much attention during the pre-match build-up.

Jill Ellis, who in this match overtook April Heinrichs' record for the most appearances as US head coach, described Rapinoe's performance as "fantastic."

"It's almost as if it just feeds her," Ellis told reporters when asked about the controversy which had surrounded Rapinoe this week.

"She's a big personality both on and off the pitch and I think she honestly thrives in these moments. There's a never-say-die attitude, she loves and lives for those moments. She's a big-time player and the bigger the stage the more she's going to respond."

The 33-year-old Rapinoe, likely to be playing her last World Cup, has now scored five goals in France, moving her level with teammate Alex Morgan and England's Ellen White at the top of the scoring charts. To illustrate the worth of Rapinoe's creativity to her country, since her World Cup debut in 2011, she has scored seven times in the tournament and provided seven assists.

Rapinoe is now the World Cup's joint top-scorer

Even before referee Kateryna Monzul had blown her whistle to start the match, US captain Morgan had raised eyebrows by not singing the national anthem. Perhaps it was Morgan's way of responding to Trump's criticism of her teammate.

The USWNT's star striker had sung the "Star-Spangled Banner" with gusto, and had also placed her hand on her heart, in the US' first four matches of this tournament. But on Friday she stood silent along with Rapinoe -- who has previously said she will probably never sing the anthem again -- in Parc des Princes.

On a day where France had experienced record-breaking temperatures, the heat did not appear to affect the tempo of a match which started at a frantic pace.

After conceding early, France worked its way back into the match, with Kadidiatou Diani posing problems on the right flank. Despite dominating first-half possession Les Bleues could not draw level, a mistimed Diani header being as close as the host got.

US players huddle at the end of the match.

The US began the second half aggressively, with Heath drawing a fine save from French goalkeeper Sarah Bouhaddi at the near post. But France created chances and looked to be gathering steam until its defense was breached in the 65th minute. Heath was given the freedom to burst down the right wing and picked out Rapinoe who was unmarked at the far post.

In the 74th minute, Heath thought she had scored her team's third of the night, but the goal was ruled out for offside and from there on in France took over, giving the impression that it might stage an unlikely comeback.

The towering Renard, unmarked inside the box, headed home Amel Majri's free-kick for the defender's fourth goal in five games. With the full-time whistle looming, France appealed for a penalty when Amel Majri's cross hit the arm of Kelley O'Hara, but the referee, rightly, ignored France's pleas and the US held on for its 10th straight World Cup win.

France, which monopolized possession, had caused the US problems, forcing Jill Ellis' into a more defensive formation in the second half, but as has been the case for France in previous tournaments, a lack of bite in attack proved to be its downfall.