Forsberg was allowed time to tee up his shot on the edge of the penalty area and, although goalkeeper Yann Sommer appeared to have it covered, Swiss defender Manuel Akanji stuck out a foot and deflected it into the corner of the net.
The last good attempt came in the 40 minute when a flawless Mikael Lustig cross found Albin Ekdal but he had left his vertical path finder at home and from six metres his first time strike didn't trouble Sommer.
The referee initially gave a penalty but changed his decision to a free-kick after a review. Then, towards the later part of the first half, Sweden began to prove themselves by finding threatening opportunities within the opposition box.
The action has continued at the World Cup with the final games from the group of 16 now decided.
Either Colombia or England will await them in the quarter-final. Of these, only the Swiss are in the top 10 of Fifa's rankings.
David Hytner's match report from the St Petersburg Stadium will follow.
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Yet Eriksson does not consider that a major issue given he thinks the team's strength to be how it functions as a unit. They have young, hungry players. "You can see our lack of experience sometimes, but we have so many qualities too".
But it was not just the Swedes who were guilty of profligacy in front of goal.
This was an earnest game of football, played by two limited sides hoping that method and organisation and endeavour would be enough to see them through.
Underestimate them at your peril.
Switzerland looked to be more intent on seizing that opportunity at the outset, controlling possession in the first half and with much of the play flowing through Xherdan Shaqiri in midfield.
On seeding, defending champions Germany would have expected to be in Samara on Saturday but they finished bottom of Group F in Russian Federation, an ignominious exit that would have come sooner had Sweden held out for a few seconds more to draw their clash in Sochi.
Both sides had been hampered by suspensions here too, with Switzerland more badly affected.
The Swiss certainly weren't playing like a team ranked sixth the world and with only one loss in their previous 25 games.
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Vladimir Petkovic's men threw a number of crosses into the box and won numerous corners without success, as the Swedes held firm at the back.
It seems to wrong to single out an individual when victory was the effect of a strong team dynamic but central defender and skipper Andreas Granqvist epitomised all that was good about his team.
Their team had just reached a World Cup quarterfinal for the first time in 24 years, and they were going to enjoy the moment.
Thus, Sweden and England defeated their rivals and will play each other in the 1/4 finals of the 2018 world Cup.
Now Shaqiri and the rest of the Switzerland team will have to go home and analyze how another round of 16 match got away from them and maybe next time end its depressing World Cup knockout curse. The Swedes, led by Janne Andersson, head into their 50th ever match at the World Cup in high spirits following a 3-0 thrashing of Mexico.
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.
Sweden's approach was the same as it has been all tournament. But unperturbed by the pressure, Swedish players kept their calm. No other player had had more without scoring.
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Besides the heat and humidity, Environment Canada is also calling for "very high" UV levels which means a higher risk of sunburn. The move is part of the federal government's climate change adaptation in expectation of more frequent heat events.
There were few clear cut chances, mostly from the Swedish attackers.