The forward scored with a header at the far post in the 33rd minute at Soccer City and added goals in the 76th and 80th minutes as Argentina moved to six points in Group B.
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Higuain had missed several clear opportunities in Argentina's opening 1-0 win over Nigeria but was confident his aim would improve.
"I knew I was getting chances but I needed to convert them," Higuain said. "Luckily, those that didn't go in against Nigeria went in today.
"It was a nice challenge to score goals. It's what a striker lives for."
After his disappointing performance against Nigeria, there was speculation coach Diego Maradona would replace him with Diego Milito. The Inter Milan striker scored both goals in the Champions League final, with Inter also winning Serie A and the Italian Cup.
But Maradona again selected Higuain, and the French-born forward returned his coach's trust against the Koreans.
"To help our team with goals is the best thing I can do," Higuain said. "We have had a great match from all points of view ... but we still have to maintain a cool head because this is just getting started."
While they have yet to score in the tournament, Messi and Tevez were both thrilled with Higuain's performance.
"I'm very happy for 'Pipa' because the goal opened up for him today. I hope he can keep it up," said Tevez, using the nickname Higuain inherited from his father Jorge, a former River Plate defender.
Messi, who was involved in all four Argentina goals, said: "It was good to see him make the most of the chances he had."
Argentina needs only a draw against Greece on Tuesday to advance to the round of 16.