Switzerland booked their place in the second round with a gutsy victory in their final Group G game in Hanover.
Frei's goal helped put the Swiss through
Hakan Yakin's pin-point cross was met by the brave Philippe Senderos who powerfully headed Switzerland in front.
Jin-Chul Choi and Chun-Soo Lee went close for South Korea before Alexander Frei scored a controversial second.
Frei rounded the keeper after the referee overruled his assistant's offside flag, ensuring the Swiss will now meet Ukraine in the second round.
The clean sheet ensured Switzerland preserved their record of not having conceded a goal in any of their group games.
And heading into the game they only needed a point to qualify.
But their high-tempo start suggested they were keen to finish the group as winners.
Frei was the first to try his luck from distance, while at the other end Ji-Sung Park tested Pascal Zuberbuhler with a low drive from 30 yards.
And Switzerland's purposeful start was rewarded on 23 minutes when the superb Yakin bent in a pin-point free-kick that Senderos comprehensively dispatched.
South Korea coach Dick Advocaat appeals to the referee
The Arsenal centre-half's courage came at the expense of a nasty cut to his face after head-butting Jin-Cheul Choi in the process of scoring, leaving both players needing treatment.
Yakin's sweet left foot from set-pieces was a constant threat for the South Koreans and shortly before the break he stung the hands of Woon-Jae Lee with a free-kick.
South Korea produced their best chance of the half when Chun-Soo Lee broke through the Swiss defence and fired in a fierce drive that was well palmed away by Zuberbuhler.
And as the lively half came to a close, Switzerland were in pole position to win the group.
The South Koreans began the second half with more zest and pegged the Swiss back in their own half, who themselves looked happy to sit back and preserve their lead.
But despite Senderos' substitution following an awkward fall on his arm, the Switzerland defence looked comfortable in repelling the South Korean attacks.
At the other end, the solitary Swiss striker Frei had two chances to kill the game, the best of which crashed against the post.
Jin-Chul Choi should have done better with a free header while Jung-Hwan Ahn shot low.
But with 15 minutes left, referee Horacio Elizondo ignored his assistant's flag to allow Frei in to slot home Switzerland's second and seal the 2002's semi-finalists' fate.
Switzerland: Zuberbuhler, Spycher, Senderos (Djourou 53), Philipp Degen, Muller, Wicky (Behrami 88), Vogel, Yakin (Margairaz 70), Cabanas, Barnetta, Frei.
Subs Not Used: Benaglio, Coltorti, David Degen, Dzemaili, Grichting, Gygax, Lustrinelli, Magnin, Streller.
Booked: Senderos, Yakin, Wicky, Spycher, Djourou.
Goals: Senderos 23, Frei 77.
South Korea: Woon-Jae Lee, Young-Pyo Lee (Ahn 62), Choi, Jin-Kyu Kim, Dong-Jin Kim, Ho Lee, Nam-Il Kim, Ji-Sung Park, Chu-Young Park (Seol 65), Chun-Soo Lee, Jae-Jin Cho.
Subs Not Used: Baek, Won-hee Cho, Chung, Do-Heon Kim, Sang-Sik Kim, Yong-Dae Kim, Young-Kwang Kim, Eul-Yong Lee, Song.
Booked: Chu-Young Park, Jin-Kyu Kim, Choi, Chun-Soo Lee.
Ref: Horacio Marcelo Elizondo (Argentina).
Fifa man of the match: Alexander Frei
This is the first time Switzerland have finished as first round group winners at the World Cup. At their last appearance in 1994, the Swiss were ousted in the second round by Spain.
Switzerland have now kept a clean sheet in three consecutive World Cup matches. They are the only team yet to concede a goal at the 2006 World Cup. The last side to negotiate the first round group phase without conceding was Argentina in 1998. The Swiss managed a first ever World Cup block-out against France in their opening fixture of this tournament, bringing to an end their unwanted all-time competition record of 22 matches without a clean sheet.
South Korea go out, having progressed beyond the group phase in only one previous World Cup - four years ago, when they were joint hosts. South Korea have now played European teams 18 times at the World Cup, winning only three times. All three victories came in 2002 on home soil.
Trivia Stats source: Infostrada Sports