Lee Jung-soo and Park Ji-sung each scored and South Korea won 2-0 over lackluster Greece in Saturday's first Group B match.
"If we had been a little bit calmer, we could have had an even better result," South Korea coach Huh Jung-moo said. "In terms of scoring goals, it could have been a little bit better for us."
Playing in its seventh consecutive World Cup — including its 2002 appearance in the semifinals, when it co-hosted the tournament with Japan — South Korea controlled the tempo from its first scoring chance on.
Greece has only been to the tournament once before, in 1994. Back then, the Greeks let Argentina score just two minutes into the opening game. The Greeks improved this time around — by five minutes.
Ki Sung-yong curled in a free kick from near the left corner flag in the seventh minute, and the ball brushed the top of Konstantinos Katsouranis' head before reaching Lee at the far post. The central defender tapped it into an unguarded net.
Park Ji-sung doubled the lead in the 52nd with a slick solo goal.
Striker Park Chu-young had another three chances to score for South Korea, and Fanis Gekas had a shot saved with 10 minutes left in what was Greece's best chance.
Greece coach Otto Rehhagel stood on the sideline at the end of the match, his hands on his hips and a fierce scowl on his face.
"We really have to get our act together," Rehhagel said. "We've got to improve a couple of things and be brave and courageous enough."
Argentina beat Nigeria 1-0 in the other Group B match.
In a stadium that was about two-thirds full, South Korea spent much of the opening minutes giving the ball away to the former European champions and defending desperately. But South Korea converted on its first opportunity.
"We conceded that really quick goal," Alexandros Tziolis said. "It took us by surprise and threw us off our game."
Rehhagel replaced captain Giorgos Karagounis at the half, but South Korea continued to dominate and Park Ji-sung made it 2-0.
"We said we shouldn't sit on our laurels and we should attack," Huh said. "I said at halftime that we would have more opportunities and we should take advantage."
Torosidis gave the ball away to Park midway inside his own half. Park surged forward and beat two sliding tackles before scoring with a low shot.
Back in South Korea, where nearly 1 million people watched the game at public gatherings, a busy Seoul boulevard turned into a sea of red with screams of joy reverberating among the tall buildings. Strangers hugged each other in elation and jumped in unison.
Greece mustered only a couple of blocked shots and appealed desperately for a late penalty when Gekas' shot hit a defender. The South Korean had his arms raised, but replays showed the ball hit his body.
Gekas then unleashed a shot from about 12 yards and goalkeeper Jung Sung-ryong punched it over the bar.
The Greeks will go for their first-ever World Cup win against Nigeria next Saturday, when central defender Vangelis Moras should be fit to return from a persistent groin injury.
"I think it was a fair result. We didn't play well," Tziolis said. "We have very few options. There's no other option than to go all out."