Julian Alvarez broke a 1-1 deadlock in the 112th minute, and Lautaro Martinez added a goal in the final seconds of extra time to send defending champion Argentina past Switzerland.
Alexis Mac Allister scored Argentina's other goal off a Lionel Messi corner, while Messi's nine-game World Cup scoring streak ended even as his bid for a second title stayed alive.
The match turned in the 67th minute when Switzerland's Breel Embolo was sent off after VAR used the mistaken-identity protocol to overturn a yellow card initially shown to Leandro Paredes.
Argentina next faces England in Wednesday's semifinal in Atlanta after the Three Lions beat Norway 2-1 earlier Saturday.