It marks a major triumph for a team that failed to get out of the group stage four years ago and now have won twice on home soil in front of jubilant crowds.
Luis Romo scored in the 50th minute after South Korea goalkeeper Kim Seung-gyu collided with defender Lee Gi-hyuk and dropped the ball inside the area. Romo easily found the open net after picking up the loose ball.
The South Koreans almost equalised in the 87th minute when Mexico goalkeeper Raúl Rangel stopped a header from close range by Cho Gue-sung, then made an even better save on the rebound, extending his right arm to keep the ball from crossing the line.
Mexico have six points from two Group A matches, three more than South Korea and five more than the Czech Republic and South Africa, who drew 1-1 earlier Thursday in Atlanta.
Mexico close their group play on Wednesday against the Czech Republic in Mexico City, while South Korea take on South Africa in Monterrey.
Mexico had never won a World Cup game on home soil outside Mexico City.
Before 2026, all but one of their nine World Cup matches at home, spanning the 1970 and 1986 tournaments, had been played at Estadio Azteca, with five wins and three draws.
When they played in Toluca in 1970, they lost 4-1 to Italy in the quarterfinals.
The top-two teams from each group progress to the knockout stage, along with the best eight third-place teams.
The round of 32 is being played for the first time at the World Cup after the tournament was expanded to 48 teams.
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