The victory, secured with goals from defender Philippe Senderos and top scorer Alex Frei, saw the Swiss finish surprise winners of Group G and moved Koebi Kuhn's men within one match of equalling the country's best World Cup showing.
If they can beat World Cup debutants Ukraine in Cologne on Monday, Switzerland will be through to the quarter-finals for the fourth time - and for the first time in 52 years.
"It's certainly possible for this team to reach the quarter-finals," said Kuhn, whose side were unique in coming through the group stage without conceding a goal.
"We can go into the next game with huge self-confidence, knowing that our opponents will also be taking us seriously now."
With just three days separating the South Korea and Ukraine encounters, Switzerland will have less time than usual to recuperate for their next challenge.
STRENGTH IN DEPTH
Friday's performance suggested however that the squad has plenty of strength in depth with teenager Johan Djourou once again proving a more than capable deputy for Arsenal club mate Senderos, who left the field in the second half after dislocating his shoulder.
Valon Behrami, who can play right back or right midfield, should be ready to start if required on Monday after recovering from a groin injury to come on as a late substitute against Korea.
Hakan Yakin has broadened Kuhn's midfield options after a show-stealing performance on his first international start in more than nine months, while first team regulars Ludovic Magnin and Marco Streller should be fresh after sitting out the win over Korea.
Finishing remains a possible weakness for the Swiss who could have wrapped up Friday's game on several occasions before Frei finally made things certain in the 77th minute.
If they can improve in that area, though, Switzerland's tight defending should be enough to see them further exceed expectations.
Italy, their likeliest quarter-final opponents who face Australia in the second round, are probably not yet shaking in their boots.
After being deservedly held to a 1-1 draw by the Swiss in a pre-tournament friendly, however, the Italians may well find themselves rooting for a Ukraine victory come Monday.
