Marcus Berg forced a fine save from Swiss goalkeeper Yann Sommer in the 27th minute, and Albin Ekdal squandered an excellent chance when he volleyed over the bar from 12 meters out after getting on the end of a cross from Mikael Lustig.
The referee initially gave a penalty but changed his decision to a free-kick after a review.
With the final action of the first period, Rodriguez crossed from the left and Olsen lost the ball but Sweden scrambled it away. How he must be gutted at missing out on a World Cup quest with the trophy there for the taking.
INCIDENTS: World Cup last 16 encounter between Sweden and Switzerland at the Saint Petersburg Stadium. The Swedish striker should have done so much better with that opportunity. This is a man who knows where the goal is.
The first presentable opportunity fell to Blerim Dzemaili after feeding off an exchange of passes in the box, but the end result skied disappointingly over the top.
Underestimate them at your peril.
Switzerland, ranked No. 6 in the world, had more possession but failed to carve out any clear-cut chances.
They were organised and obdurate, playing with a discipline that allowed them to frustrate the Swiss and try to strike on the counter.
With both teams attacking fiercely, none of them found the back of the net in first 30 minutes of the match.
Brazil and Serbia both scored early, which meant Switzerland could grow into the game as it went on; both sides sat in and kept their shape.
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Belgium were emphatic in the second half, but right before Chadli's goal, Japan actually had a short spell of dominance. I just want to play and I help my team-mates, I have to help my team and that's what I am here for, nothing else.
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Mercedes driver Valtteri Bottas started from pole position ahead of his team mate Lewis Hamilton . Hamilton insisted that they should have won the race. "It's just the way the sport is".
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With World Cup hopes fading, Switzerland tried to force an equaliser.
It seems to wrong to single out an individual when victory was the outcome of a strong team dynamic but central defender and skipper Andreas Granqvist epitomised all that was good about his team.
Sweden has reached the knockout stage at each of their last four World Cup appearances.
They will now await the victor of Colombia or England and, having seen off the Netherlands and Italy in qualifying, and then finished above Germany in Group F, Andersson says there is still more to come.
Forsberg has been Sweden's most promising player at this World Cup, but up to now has only shown glimpses of his true quality. Ekdal from a similar position from where they opened the scoring, evaded Granit Xhaka's challenge but then fired over.
Sweden are unbeaten in their last three games against Switzerland (W1 D2) although their last encounter was in March 2002 (1-1).
Emil Forsberg's deflected effort had earlier sent Sweden through to the last eight for the first time since U.S. 1994 as they edged Switzerland in an intriguing last 16 tie.
"We have to be ready to play really from the get-go in such a way to have the initiative on our side", coach Vladimir Petkovic said Monday through an interpreter.
"If we've played 120 minutes we have a clear plan in place of what we're going to do, but I'm not going to enter into any more details".
"We should have done things better but we weren't good enough to win the match". "Over the past matches that I've seen with the Swedish team, all the opponents have had a hard time developing those emotions when they were on the pitch against them".