Switzerland's Yann Sommer saved France striker Kylian Mbappe's penalty to secure a 5-4 shootout win over the world champions following a thrilling 3-3 draw after extra time on Monday to reach the Euro 2020 quarter-finals where they will meet Spain.

On a memorable evening for Swiss football, the so-called Nati repeatedly beat the odds, coming from 3-1 down with two goals in the final five minutes to force extra time and eventually penalties.

It was Switzerland's first knockout stage victory at a tournament since 1938 and the first time they have made the last eight since the 1954 World Cup which they hosted. They will next face Spain on Friday in St Petersburg.

"Honestly I am still in shock," said Sommer, who became the most capped Swiss keeper with 65 international appearances.

"We showed courage, heart, we left everything out there. When you come back from two goals down against the world champions it is just unbelievable, and then to win on penalties, I could not be prouder of the way we did it."

France, who had started with an unusual three-man defence and lacked any real bite up front in the first half, looked to be heading for victory when Karim Benzema struck twice in two minutes early in the second half.

He latched on to Mbappe's through ball in the 57th minute to cancel out Switzerland's first-half lead from Haris Seferovic's header.

Benzema then headed home from near the goal-line two minutes later to take his tournament tally to four as France grabbed control of the game only minutes after the Swiss missed a 55th minute penalty and the chance to go 2-0 up when Hugo Lloris saved Ricardo Rodriguez's spot kick.

By the time Paul Pogba curled a sensational shot into the top corner in the 75th minute to make it 3-1 for France, who had reverted to a four-man backline in the second half, few believed the momentum could shift once more.

"Nobody believed in us anymore at that stage," Sommer said. "But before the game we had said no matter what happens in the game, it doesn’t matter if we’re down, or if things are going well, we play until the end.

"We felt France had become a bit complacent and maybe thought they had already won it. So we used that to our advantage."

Seferovic sneaked into the box again to head in his second goal with five minutes left and substitute Mario Gavranovic beat Lloris to snatch a 90th-minute equaliser and force extra time after France substitute Kingsley Coman's drive hit the bar.

Olivier Giroud twice came close for France having come off the bench but the game was to be resolved on penalties where Sommer swatted Mbappe's spot kick away after five Swiss players had scored to earn their first ever tournament shootout win.

The result means France coach Didier Deschamps will miss out on becoming the first man to win World Cup and Euro titles both as a player and a coach.

"It is my responsibility and I told the players that I assume it," Deschamps, who won the 2018 World Cup with France, said of the shock loss.

"When France win merit goes always to the players. When things are less good then it is my responsibility. But that's the way sport is. You have to accept it even if it hurts."