Emil Forsberg’s deflected strike has sent Sweden through to the quarter-finals of a World Cup for the first time since 1994.
The last-16 tie had been locked at 0-0 for 66 minutes of the game before Forsberg’s shot trickled past Switzerland goalkeeper Yann Sommer.
The match ended in chaos when Switzerland’s Michael Lang was sent off for a push on Martin Olsson late in the game.
Sweden will play either England or Colombia in the last eight of the World Cup in Samara on Saturday afternoon.