The Albiceleste beat South Korea 4-1 on Thursday as their fans outcheered the vuvuzelas, giving them six points off two victories in Group B.
Argentina is alone in first place, three points ahead of both South Korea and Greece with a game left in group play. The Greeks beat Nigeria 2-1 later Thursday.
"I have to congratulate the players ... everything they did worked out well," Argentina coach Diego Maradona said. "I am very happy."
In a biting wind, Maradona's team put on one of the best performances of the tournament, perhaps only challenged by Germany in its 4-0 win over Australia.
The Argentines had 11 shots on goal to just two for South Korea and controlled possession for 57 percent of the match.
"I wanted to have my players focused like today," said Maradona, who as a player took Argentina to a World Cup title in 1986.
The Argentines took the lead in the 17th minute when Park Chu-young deflected in a free kick from Messi. Higuain made it 2-0 in the 33rd after Nicolas Burdisso passed along a cross from Maxi Rodriguez.
In first-half injury time, Lee Chung-yong pounced on a defensive mistake to close the gap, but Higuain's two second-half goals — in the 76th and 80th minutes — put the game away.
Messi made a great run to set up Higuain's second goal. He had a shot blocked, got the rebound and hit the post with a second strike. The ball bounced to Higuain, who tapped it in. Four minutes later, Messi played the ball in to substitute striker Sergio Aguero, who crossed for Higuain to complete the rout.
"I'm very happy to score the goals, but we have to think of the team as a whole," said Higuain, now the tournament's leading scorer.
Early in the second half, the South Koreans made a surge and for a short time seemed poised to tie the game. In the 58th minute, Yeom Ki-hun almost scored the tying goal, but his shot went just wide of the left-hand post.
The rally didn't last.
The crowd at Soccer City was overwhelmingly pro-Argentina, with blue and white banners ringing the stadium and fans singing and chanting throughout the game — for once, drowning out the buzz of vuvuzela horns that have become this World Cup's symbol.
Fans behind the Argentina bench released blue and white balloons as the team took the field. Maradona, ever the entertainer, gave one a playful kick.