Emil Forsberg struck the decisive blow midway through the second half with a strike that deflected off the luckless Manuel Akanji and left Yann Sommer stranded in the Swiss goal.
Sommer had brilliantly clawed away a shot on the turn from Marcus Berg in the first half and denied Haris Seferovic late on but it was undoubtedly a game that was more about missed opportunities than good saves.
Both sides were guilty of squandering good openings - and Switzerland ended it with 10 men after Michael Lang was dismissed in injury time for a push on Martin Olsson, who was clean through on goal.
The referee initially gave a penalty but changed his decision to a free-kick after a review.That will not bother the Swedes, who have reached the last eight of this competition for the first time since 1994.
The bottom half of the draw at the World Cup offers a superb opportunity for a relatively unfancied team to reach the final.
Going into Tuesday's two remaining last-16 ties, one of Switzerland, Sweden, England, Colombia, Croatia and Russia was certain of reaching the final. Of these, only the Swiss are in the top 10 of Fifa's rankings.
And while the match in St Petersburg could not be said to lack passion or goalmouth incidents, the quality of finishing gave the impression that neither side was capable of taking the glorious opportunity in front of them.
The worst miss was by Sweden's Albin Ekdal, who was superbly picked out by Mikael Lustig's beautifully weighted cross but horribly ballooned his strike well wide. A header would have been a much better option.
Striker Marcus Berg snatched a shot off target too after Ola Toivonen's deft flick created the opening and had another effort blocked.But it was not just the Swedes who were guilty of profligacy in front of goal.
Steven Zuber was off target with a near-post header and later exchanged a series of passes with Blerim Dzemaili, who had a great opening from 16 yards but again showed a lack of composure that let the game down at key moments.
