Janne Andersson's men lost to a stoppage-time goal against the Germans on Saturday, but a 3-0 win over Mexico and Germany's shock 2-0 reverse against South Korea gave the Swedes a last 16 tie against Switzerland.
Following the final whistle, fans and pundits quickly scanned the possible opponents further down the line, with many immediately predicting another run to the semi-finals, just as they did in 1994.
"If we manage that (beat Switzerland), then it's England in the quarter-finals -- and for an Englishman, it is physically impossible not to underestimate Sweden," said Aftonbladet journalist Robert Laul.
"After that, we're in the semi-final against Spain or Croatia - a new '94 summer," Laul concluded.
The 1994 side may have boasted some more skilful goalscorers in the form of Tomas Brolin, Martin Dahlin and Kennet Andersson, but the game plan in the American heat was the same as here in Russia - defensive organisation and hard running.
Then-coach Tommy Svensson and incumbent Andersson are similar, no-frills managers steeped in the Scandinavian nation's soccer tradition who prize the well-being of the collective over all else.
Unlike the fans and pundits, Andersson is taking nothing for granted.
"Switzerland are a strong team, no doubt about it. They won nine of ten games in qualifying and went through their group unbeaten here," he said as the team returned to its base on the Black Sea coast to prepare for the next game.
"We now have a few days to do a detailed analysis and in time decide a game plan," he added.
Sweden's best World Cup performance came when they hosted the 1958 competition, losing the final to Pele's Brazil. But the epic journey of 1994 is still fresh in the memory for many of the fans now scrambling for tickets for the last 16 game in St Petersburg - a mere hour's flight from Stockholm.
"You can count on the Golden Wall (of Swedish fans) dominating in the stands when all of Sweden hopes for new heroic blue-gold matches," wrote Daniel Kristoffersson in the Expressen newspaper.
(Reporting by Philip O'Connor; Editing by Christian Radnedge)
