It was Lang who brought down Olsson as he raced through on goal and he has been shown a red card.
Sweden grabbed a last eight ticket following their 1-0 win over Switzerland in the round of 16 at the ongoing World Cup in Russian Federation at the St. Petersburg Stadium on Tuesday.
It was an encounter both side could have won but the level of finishing was poor until Frosberg's deflected strike from distance in the second half proved to be the difference.
Sweden will now play the victor of Tuesday's other round of 16 duel between England and Colombia in Samara on July 7, with a place in the last four at stake.
Both teams created numerous chances in what was an end to end first-half.
Sweden were making their 50th appearance at the World Cup finals as they took on the Swiss, a feat which meant that only Mexico had made more appearances than them in the tournament without winning the competition.
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Marcus Berg, who has been industrious but not scored in this tournament, had two brilliant opportunities.
The same player had also volleyed over earlier in the half too.
The desperate Swiss, looking for an equaliser were hit by a counter as Martin Olssen latched on to a through ball. He played in Berg whose shot was blocked brilliantly by Manuel Akanji, before Ekdal's rebound was off target.
Switzerland coach Vladimir Petkovic: "We're sorely disappointed, the whole team is".
Blerim Dzemaili took a shot well over the Sweden crossbar, but he got the ball on top of the box from a good build-up with scores remaining 0-0 after 38th minutes of action.
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In the first minute, after Sweden had lost possession, Xherdan Shaqiri drilled a speculative strike wide from outside the area. His "performance" during the World Cup is a joint project on bolstering tourism to St. Petersburg and the Hermitage Museum.
Yes, Switzerland did enjoy the bulk of possession, including nearly a dozen corners, but the Swedes' defence was always in the way.
As expected there was late pressure from the Swiss.
On the 21st minute Shaqiri delivered another long cross-in, but it was calmly collected by Sweden keeper Robin Olsen. Ricardo Rodriguez crossed a ball into the box but the Swiss striker's header was denied by Olsen. He went down in the penalty area but the first contact, as shown by VAR, was just outside the penalty area.
Toivonen's curling effort from the resultant set piece was then saved by Sommer with the last kick of the match.
Although not convincing in front of goal, the Swede's were dogged again in their performance and deserved a place in the last eight.
A merry band of about a thousand yellow-clad Sweden fans stayed after the game, singing in a stand behind the goal and ignoring repeated requests from the stadium announcer to make their way out.
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The Swiss have twice conceded the opening goal in Russian Federation - first in their 1-1 draw with Brazil and again against Serbia - when Switzerland became the first team at this World Cup to win after going a goal down.