The Manchester United midfielder struck seven minutes after the break at the Nelson Mandela Bay Stadium in Port Elizabeth to double his side's advantage following central defender Lee Jung-soo's seventh-minute opener.
Huh Jung-moo's side ultimately ran out comfortable winners in front of an army of their delighted fans among a crowd of 31,513 as Greece's fourth World Cup finals outing ended in the same way as the pervious three, with defeat and without a goal scored.
Coach Otto Rehhagel had warned his players in advance to beware South Korea's panther-like qualities, and by the time he got them back into the dressing room at the break, he will have been relieved they had not been mauled further.
It took Korea just seven minutes to get their noses in front in the Group B encounter when Lee Jung-soo met Celtic midfielder Ki Sung-yueng's swinging free-kick unopposed and volleyed it gleefully into the back of the net.
Greece's woes might have increased further with Bolton's Lee Chung-yong astonished not to be awarded a 15th-minute penalty for a clumsy challenge from behind by full-back Vasilis Torosidis as referee Michael Hester waved play on.
But it would have been 2-0 with 28 minutes gone had defender Avraam Papadopoulos not got in a last-ditch challenge on striker Park Chu-young as he shot to allow keeper Alexandros Tzorvas to make a vital block.
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Greece had started the game brightly, Torosidis firing wide when he met skipper Georgios Karagounis' second-minute corner with an instinctive half-volley, but it was largely downhill from there.
The anticipated aerial onslaught never materialised as central defenders Lee Jung-soo and Cho Yong-Hyung coped admirably with front two Theofanis Gekas and Angelos Charisteas.
By contrast, Korea were enterprising in their movement and strikers Park Chu-young and Yeom Ki-hun, with support from a fluid midfield quartet, kept the Greek defence at full stretch.
They increased their lead within seven minutes of the restart when Park Ji-sung made the most of Loukas Vyntra's woeful control in the middle of the park to race in on goal, leaving the central defender and partner Papadopoulos for dead before sliding a shot across Tzorvas and into the bottom corner.
Rehhagel, who had replaced Karagounis with Christos Patsatzoglou at the break, withdrew Charisteas and Georgios Samaras in quick succession and asked Dimitrios Salpingidis and Pantelis Kapetanos to find a way back into the game.
But Park Chu-young headed just over from full-back Cha Du-ri's 63rd-minute cross as the Koreans threatened to run riot.
Gekas acrobatically fired high over after controlling a long ball well on his chest with 68 minutes gone and Salpingidis headed weakly at the keeper two minutes later with time fast running out for Greece.
The Hertha Berlin frontman forced a fine one-handed save from Jung with a left-foot shot on the turn with nine minutes remaining, but Yeom, Lee Chung-yong and Kim Jung-woo all went close at the other end as time ran down.