After a goalless first half, a deflected effort from Emil Forsberg got the job done for Sweden, who reach the last eight of this tournament for just the second time since 1958.
Switzerland had Michael Lang dismissed during the closing stages of the game for a professional foul but it mattered little as Sweden saw out the remaining seconds to secure a showdown with either Colombia or England.
During the opening stages of the game, both Xherdan Shaqiri and Steven Zuber failed to threaten with long-range strikes and Sweden almost capitalised when Marcus Berg was played through on goal, only for the forward to slice a half-volley well wide of the target.
Albin Ekdal also drilled a shot over for Sweden as they began to get themselves on top but the game quickly developed into a contest of few clear-cut opportunities.
Nevertheless, just before the half-hour mark, Sweden almost went in front through Berg but Switzerland stopper Yann Sommer made an excellent save to his right from a volley.
With six minutes remaining before the interval, Blerim Dzemaili was teed up for Switzerland's best opportunity of the half but the Bolgona playmaker sent his first-time effort from a central position over the bar.
However, Sweden should have gone ahead moments later as Ekdal was found at the back post but the midfielder sent a volley from no more than eight yards harmlessly over Sommer's bar.
After the restart, Sweden continued to show the greater threat in the final third but they wasted another opening when Ola Toivonen volleyed over the crossbar after a knockdown inside of the area.
The match quickly became one-paced with both teams seemingly wary about conceding the opening goal, but Sweden found a way to break the deadlock midway through the second half through Forsberg, whose shot from the edge of the box was deflected into the top corner by Manuel Akanji.
The opener forced Switzerland to show more ambition in the final third but as the game entered the final quarter-of-an-hour, Vladimir Petkovic's team were still looking to trouble Robin Olsen for the first time.
Substitute Breel Embolo was bringing an extra threat and the Schalke 04 attacker got up well to meet a corner, only for Forsberg to clear off the line with Olsen behind him.
Haris Seferovic forced Olsen into a save with a powerful header as three minutes of added time were signalled but in the final minute, Switzerland were reduced to 10 men as Lang was dismissed for a professional foul on Martin Olsson.
Toivonen saw the resulting set piece saved by Sommer but the referee blew his whistle as Sweden registered their third victory and clean sheet of the tournament.
SWEDEN (4-4-2): Olsen; Lustig (Krafth 82'), Lindelof, Granqvist, Augustinsson; Claesson, Svensson, Ekdal, Forsberg (Olsson 82'); Berg (Thelin 90'), Toivonen
SWITZERLAND (4-2-3-1): Sommer; Lang, Djourou, Akanji, Rodriguez; Behrami, Xhaka; Shaqiri, Dzemaili (Seferovic 73'), Zuber (Embolo 73'); Drmic