The hosts had not lost an international fixture since a 3-1 defeat to Bosnia-Herzegovina on March 22 last year, but goals from Park Chu-Young and Son Heung-Min either side of half-time ended Greek hopes of a blemishless 12 months in Piraeus on Wednesday.
Fernando Santos' charges hit the woodwork on three occasions to make defeat even more difficult to take, as the 2004 European champions were dealt a blow in their preparations for the 2014 FIFA World Cup.
The visitors - also heading to Brazil in June - started brightly, and Lee Chung-Yong was sent clean through on goal by Park in the eighth minute, but was denied by the legs of debutant goalkeeper Panagiotis Glykos from close range.
And it was Park who made the breakthrough 10 minutes later as he met a wonderful chipped pass from Son in the penalty area to fire beyond Glykos.
Greece should have been level soon after, when Jose Holebas whipped a superb cross into the penalty area, only for Konstantinos Katsouranis to direct it against the right-hand post.
The hosts had the frame of the goal rattling twice more on the half-hour mark - first as Vasilis Torosidis headed against the crossbar from a powerful Georgios Samaras shot, and secondly when Avraam Papadopoulos struck the woodwork from the rebound.
Greece were beginning to dominate, and Konstantinos Manolas headed just wide of the left-hand post from a Holebas corner shortly before the interval.
Despite the Greeks showing signs of finding a way back into the match, it was the South Koreans who dealt the next blow as Son rifled a close-range effort into the roof of the net 10 minutes into the second period.
Substitute Ioannis Fetfatzidis attempted to pounce when the visiting defence failed to clear its lines 15 minutes from time, but blasted high and wide from inside the six-yard box, before Lazaros Christodoulopoulos skewed an effort wide of the target as Greece struggled to make any progress in reducing the deficit.
