The last time Sweden made it this far at the World Cup was in 1994, when the team reached the semifinals. But the goal made the difference for the Swede side who are yet to taste defeat since the start of the Russian Federation showpiece.
The World Cup Round-of-16 match between Switzerland and Sweden on Tuesday will be a duel between Europe's two quiet, under-the-radar achievers.
The RB Leipzig midfielder neatly worked space for a shooting opportunity on the edge of the box 24 minutes from time, but still needed a slice of fortune to set up a last-eight meeting with England or Colombia as his shot deflected off Manuel Akanji to leave Yann Sommer stranded.
While Switzerland's strength lies in their solidity at the back, they also carry an attacking threat, led by their skilful playmaker Granit Xhaka and winger Xherdan Shaqiri.
They were organised and obdurate, playing with a discipline that allowed them to frustrate the Swiss and try to strike on the counter.
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Only had 22 touches over the 90 minutes.
Sweden finished ahead of the Netherlands in their qualifying group and then defeated Italy in a play-off tie to reach the World Cup.
Back came Sweden, winning a risky free kick about 30 yards out, Forsberg seeing his effort deflect off the wall and past the far post.
Forced to play wide left of the midfield four rather than his favoured position in a central playmaking role that has seen him shine in the Bundesliga, Forsberg was often reduced to covering the ground than getting on the ball in Sweden's three group games. They just didn't have the quality to break down the Swedish rearguard; Blerim Dzemaili wasn't almost as impactful with his late runs into the box, and Xhaka seemed to be playing without goal, as he is often criticised for doing at Arsenal.
It was fortunate, but no more than Sweden deserved.
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The veteran Barcelona midfielder came off the bench and nearly won the game with an 85th-minute shot well saved by Akinfeev. Nonetheless, Artem Dzyuba was able to draw a penalty from Gerard Pique who was called for a handball just inside the box.
Before this game, Switzerland coach Vladimir Petkovic dismissed suggestions that this is the weaker side of the draw.
And when at the end the Swiss pressed for an equaliser, Forsberg cleared from close to his goal and several team-mates put in desperate blocks as they showed that they will provide a hard test for anyone who wants to stop them reaching the final. Steven Zuber, scorer of the equaliser against Brazil, started, but he couldn't emulste the 21-year-old's direct running.
And Switzerland's lack of creativity in the middle helped them by and large. But they were caught out on Tuesday, their first plan didn't work and they had nowhere to go. The Swedes will next play either England or Colombia on Saturday in Samara.
This will be the first time the two teams meet at a major tournament.
Denmark - World Cup - 1 July 2018
The Danes will look for Christian Eriksen to lead the attack against Croatia . 39 minute: Free-kick to Croatia on the left-flank. Schmeichel makes another save, but this time the rebound falls to Perisic - his shot goes over the bar for a goal kick.
Switzerland's Ricardo Rodriguez also missed a sitter in the 32nd minute from a free-kick but Olsen, the Sweden keeper held on. They have the basics covered, but must learn to take more risks if they are to move forward successfully into the Nations League and, looking at the bigger picture, Euro 2020.