Emil Forsberg's deflected second-half strike downed Switzerland and sent Sweden into their first World Cup quarter-final since 1994.
Switzerland looked the better side in an uninspiring first half but failed to convert the few chances they created, and Sweden midfielder Emil Forsberg broke the deadlock 66 minutes in.
Forsberg's powerful but seemingly unthreatening strike from the edge of the box was deflected off defender Manuel Akanji's left foot to leave goalkeeper Yann Sommer helpless.
Switzerland pushed for an equaliser in the closing stages of the game but their hopes of a comeback were ended after defender Michael Lang was shown a straight red card with seconds to go for bringing dow Swedish substitute Martin Olsson when he was clean through on goal.
The referee initially pointed to the spot, only to overturn his original decision after consulting the VAR system. Sommer saved the ensuing free-kick, upon which the final whistle was blown.
Sweden last played in the last eight at the 1994 FIFA World Cup in the United States, where they eventually finished third.
Janne Andersson's side will next play England or Colombia in Samara on Sunday morning (AEST).