The match was turned on its head when substitute Mario Gavranovic snatched a 90th-minute equaliser and force extra time.
Yann Sommer saved France striker Kylian Mbappe's spot kick to give Switzerland a 5-4 penalty shoot-out win, following a thrilling 3-3 draw after extra-time, on Monday as they advanced to the Euro 2020 quarter-finals where they will meet Spain.
Kylian Mbappe missing the decisive kick in the shootout as world champions France were eliminated from Euro 2020 by Switzerland on Monday encapsulated the biggest lesson of an extraordinary night -- you cannot rely on individual brilliance alone.
Spain prevail in shootout against gallant 10-men Swiss
Finland claimed a shock 1-0 Euro 2020 victory over Denmark in their first major tournament appearance
The result shook up League A Group 4, giving Ukraine an outside chance of finishing top of the group with two games remaining.
Portugal had to settle for a 0-0 draw at home to Spain in a heavyweight friendly on Wednesday after hammering the crossbar twice and missing a last-gasp open goal.
Romelu Lukaku scored twice to earn Belgium a 2-1 victory over Switzerland in the Nations League on Friday, lifting the mood in the country after a week marred by match-fixing allegations.
Sergio Ramos equalled Iker Casillas's record of 167 appearances for Spain on an emotional night at Sporting Gijon's El Molinon stadium, which paid tribute to the late Spain and Sporting forward Quini before kickoff.
This and more from the happenings in the world of football
A round-up of Tuesday night's matches in the UEFA Champions League.