The Koreans, who reached the semi-finals in 2002 as co-hosts, scored a goal in each half to deliver a strong message to their group rivals with a slick and confident performance to mark their eighth appearance in the finals.
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"We played to win and our players worked really hard," said South Korea coach Huh Jung-moo, the first Korean to manage a World Cup side since 1998. "The team played well and the flow of the game was very good," he said.
"In the second half we made two huge mistakes," he said. "I knew the Koreans would be very fast, very swift and they would run the extra mile to get the ball. It was a well-deserved win."
Greece started brightly and could have scored in the third minute when Vassilis Torosidis steered Giorgos Karagounis's corner past the post with the Korean defence all at sea.
They snatched the lead in the seventh minute when Lee Young-pyo's corner drifted past four defenders into the path of Lee Jung-soo, who volleyed the ball into the net to spark frenzied celebrations from thousands of travelling Korean fans.
Park Chu-young looked certain to double their lead near the half-hour mark when Park Ji-sung's incisive pass put him clean through on goal, only for his shot to clip goalkeeper Alexandros Tzorvas and spiral over the bar.
Park Ji-sung, uncharacteristically quiet in the first half, burst into life after the break and doubled South Korea's lead in the 52nd minute to deal a killer blow to Greece.
