Following a thrilling 3-3 draw after extra time on Monday, Switzerland's Yann Sommer stopped France forward Kylian Mbappe's penalty kick to secure a 5-4 shootout win over the world champions, advancing to the Euro 2020 quarter-finals, where they will face Spain.
It was Switzerland's first knockout stage triumph since 1938, and the country's first appearance in the final eight since hosting the 1954 World Cup.
The so-called Nati came back from a 3-1 deficit with two goals in the closing five minutes to force extra time and then penalties on a momentous evening for Swiss football.
When Karim Benzema scored twice in two minutes early in the second half, the French appeared to be on their way to win.
In the 57th minute, he latched on to Mbappe's through ball to cancel out Haris Seferovic's first-half header for Switzerland.
Following a sluggish first half, France took control of the game, minutes after the Swiss had missed a 55th-minute penalty. Benzema then headed home from near the goal-line two minutes later to take his tournament total to four as France took control of the game, following a mediocre first half.
Hugo Lloris stopped Ricardo Rodriguez's penalty kick as the Swiss squandered an opportunity to grab a two-goal lead at a crucial juncture in the game.
Few felt the momentum could turn again by the time Paul Pogba made it 3-1 for France with a spectacular curled shot into the top corner in the 75th minute.
However, with five minutes remaining, Seferovic headed in his second goal, and replacement Mario Gavranovic beat Lloris to clinch a 90th-minute equalizer and force extra time as France substitute Kingsley Coman's shot sailed over the bar.
After five Swiss players scored, Sommer blasted Mbappe's spot-kick away to claim Switzerland's first-ever competition shootout victory.