The victory, following their impressive opening 1-0 win over Nigeria on Saturday, virtually guaranteed their place in the second round as they tightened their grip at the top of Group B.
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Higuain's hat-trick, the first at these finals, comprised two headers plus a tap-in and, while he basked in the spotlight afterwards, every man played a part in an excellent performance.
World Player of the Year Lionel Messi and his attacking midfield sidekick Carlos Tevez were again inspirational.
"Korea were never capable of controlling us," said Argentina coach Diego Maradona. "Of course, they scored but they were never able to dominate any part of the match.
"I have 23 top players and they are all ready to put on the jersey and work on the pitch and that makes you happy and then you have peace of mind," he added.
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Argentina, seeking a third title after triumphs in 1978 and 1986, could take heart from the performance of substitute Nicolas Burdisso who was outstanding in defence after replacing the injured Walter Samuel in the first half.
Argentina's display, choreographed by their increasingly theatrical coach, was well worth the entrance fee and is a show no-one should miss in the weeks ahead.
The only serious mistake came just before half time when defender Martin Demichelis, who otherwise had a fine game, failed to control a simple ball from which Korea scored.
Apart from that, Maradona's side played with a silky confidence and authority the Koreans could not handle.
They did not have it all their own way however.
LAST KICK
After going 2-0 behind inside 33 minutes, Korea came back into the game with the last kick of the first half when Lee Chung-yong capitalised on Demichelis's mistake to make it 2-1.
Maradona was philosophical about the error, saying: "It can happen to anybody and didn't effect us in any way. On the contrary, this made us stronger. Apart from that mistake Korea were never able to have possession or control the match."
However, in the 58th minute South Korea winger Yeom Ki-hun should have made it 2-2 when he fired wide with only goalkeeper Sergio Romero to beat after a swift Korean counter-attack.
That was their last chance, though, as Argentina tightened their grip on the game and powered through for victory.
The opening goal after 17 minutes was lucky as the ball bounced
