Fans in Bucharest were treated to a European Championships classic as Switzerland held France to a 3-3 in normal time before beating them 5-4 on penalties.
The world champions looked stagnant in the opening half and were made to pay as Haris Seferovic headed Switzerland in-front.
There was little response from Didier Deschamp's side who looked a shadow of the team that topped the tournament's group of death.
Their slow start continued in the early minutes of the second half as the Swiss came close to a second goal.
Benjamin Pavard's aggressive tackle in his own penalty area led to a Switzerland penalty. Ricardo Rodriguez stepped up but was denied form the spot by a brilliant save from Hugo Lloris.
The save seemed to wake the French players up as the threat of elimination began to loom.
A re-energised French outfit quickly went on the front foot and it didn't take long for them to find a breakthrough.
Karim Benzema bagged two goals in a space of three minutes to turn the game completely on its head.
The Real Madrid man, who has now scored four goals in the tournament, put the French in control for the first time in the match.
With 75 minutes on the clock, Paul Pogba shocked the continent by producing one of the greatest goals in Euros history.
The Manchester United midfielder received possession just outside of the area and decided to have a go from distance. The ball flew into the far reaches of the top corner as the National Arena came unglued.
However, the drama was far from over.
With ten minutes remaining, Seferovic headed in his second goal of the game to give the Swiss late hope.
That hope soon turned into reality as Mario Gavranovic found the back of the net with a long-range effort. His 90th minute equaliser sent the game into extra time.
Despite producing a number of goalscoring opportunities, France were unable to break the deadlock during the 30 additional minutes. This meant that the winners would be decided via a penalty shoot-out.
Gavranovic - who scored the late equaliser - opened the scoring by sending Lloris the wrong way. Pogba levelled things up by doing the same.
Fabian Schar and Olivier Giroud both calmly converted to make it 2-2. Manuel Akanji and Marcus Thuram both scored to make it 3-3 although their efforts looked a little less convincing.
Lloris was able to get his hand on Ruben Varga's effort however he couldn't keep the ball out. Presnel Kimpembe, meanwhile, powered his effort confidently past Yann Sommer.
Admir Mehmedi successfully converted Switzerland's fifth penalty meaning Kylian Mbappe needed to score in order to keep his side in the contest.
The 22-year-old struck the ball with power but was ultimately denied by Sommer who sent Switzerland into the quarter-final.
Read the full report on our sister site, Football365.
Stat of the day
From OptaJoe: There were just 4 minutes & 3 seconds between Hugo Lloris' penalty save and Karim Benzema's second goal putting France 2-1 up.
Following a dramatic night in Bucharest, Switzerland will now turn their attention to Spain.
The blockbuster quarter-final will take place in Saint Petersburg on Friday, June 2.
The two nations have produced some of the most memorable moments in the sport and another dramatic encounter is expected in London.
The two sides last met at Euro 2012 when Andriy Shevchenko scored a seven-minute brace to seal a 2-1 win in Kiev.
The former striker - now turned Ukraine manager - will be looking to lead his side to victory once again.