Higuain scored his first goal in the 33rd minute with a far post header after Nicolas Burdisso flicked on a cross from Maxi Rodriguez. He added two second-half goals - in the 76th and 80th minutes - to put the result beyond doubt.
"I have to congratulate the players ... everything they did worked out well," Argentina coach Diego Maradona said. "I am very happy."
Argentina had gone ahead 1-0 in the 17th when Park Chu-young deflected a free kick from Lionel Messi into his own net, and looked to be comfortable after Higuain's header. But South Korea pulled one back in first-half injury time when Lee Chung-yong pounced on a defensive mistake by defender Martin Demichelis.
Argentina now leads Group B with six points from two games, while South Korea, which beat Greece 2-0 in its opening match, has three. Greece beat Nigeria 2-1 Thursday to also have three, while the Nigerians have zero.
With Messi playing in a slightly deeper role, Argentina lacked a cutting edge in the opening stages, its main threat coming down the left wing where Carlos Tevez was drifting into space and linking well with Gabriel Heinze and Angel Di Maria.
Higuain, who missed a string of chances against Nigeria, shot high over the bar in the eighth minute and Messi only showed occasional flashes of brilliance as he was man-marked and often found himself closed down by two or three opponents.
However, the South Korean tactics of targeting Messi, so influential in Argentina's opening match, freed up Tevez, and the combative Manchester City striker was his team's main inspiration in the first half.
South Korea came close to scoring in the 26th when Ki Sung-yong sent in a swerving shot from outside the box that just cleared the crossbar.
Two minutes later, Messi backheeled a free kick to Tevez, who sent a powerful shot just over the bar.
The match was played in a cold wind, and the South Koreans emerged with more confidence in the second half after they had pulled a goal back.
In the 58th, Yeom Ki-hun almost equalized following a flowing counterattack but put his shot just wide of the left-hand post.
Maradona brought on striker Sergio Aguero in the closing stages, and with 14 minutes left Messi - increasingly breaking free of his markers - skipped past two challenges and shot against the post, but Higuain was on hand to tap in the third goal.
Four minutes later, Messi played in Aguero, who crossed for Higuain to head in the fourth.
Higuain, now the tournament's leading scorer, said he was delighted to lead his team to victory. "I'm very happy to score the goals, but we have to think of the team as a whole."
Maradona refused to be drawn on which teams Argentina might encounter later in the competition, preferring to focus on his team's performance.
"We deserved this triumph because this was the type of outcome we'd hinted at achieving against Nigeria. And this time it happened."
He refused to criticise Demichelis for his defensive error, and said conceding the late goal had a positive effect.
"It emboldened the team because in the second half they came out with a strong attitude - they did it for a teammate who had made a mistake."
