The Real Madrid striker grabbed the first hat-trick of the FIFA World Cup™ to help his country ease to a 4-1 win at Soccer City.
The win took Diego Maradona's men to the brink of qualification from Group B following their opening triumph over Nigeria and with a game against Greece still to come.
Argentina, who held a two-goal lead until the closing stages of the first half in Johannesburg, conceded a goal that then seemed to expose their defensive frailties. But Budweiser Man of the Match Higuain had no doubt there was only one side that was going to win.
"It was a tough match indeed and we knew it was going to be difficult, but we managed to play our way," he said. "We were fighting to win it and our intentions were clear.
"We played our style and that's what brought us to this victory. We won deservedly and we're going to continue to play our style."
It was an ominous warning for the rest of their FIFA World Cup opponents, who may take heart from the way the Koreans played early in the second half.
Higuain added: "I think all in all it is a very positive result. We played a great game, no doubt the goal against us put on some pressure, but we knew that we would get more chances to score. We're happy about this match, but at the end of the day we're not too overly euphoric."
Asked how he felt about heading the goalscorers race in South Africa, the 22-year-old said: "It is of course a major challenge, but the important thing is to think about the team.
"With the team we have had a great match, we were able to score and that was what we were aiming at. So this of course makes me happy to be on the top, especially when you can win and do something for the team."