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.
"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.
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.
Apart from that, Maradona's side played with a silky confidence and authority the Koreans could not handle.
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."
