GUADALAJARA, Mexico, June 18 : Mexico beat South Korea 1-0 in the World Cup on Thursday to win Group A, with Luis Romo's second-half goal securing the hosts their place in the knockout stage.Mexico broke through five minutes into the second half after the South Korean goalkeeper, Kim Seung-gyu, made a costly error when he failed to gather a cross after colliding with a teammate, allowing Romo to volley into an unguarded net.Kim later made amends with a save to deny Raul Jimenez, while Raul Rangel in the Mexican goal brilliantly stopped a late attempt from Yang Hyun-jun to preserve Mexico's clean sheet.The result leaves Mexico on six points to qualify as Group A winners. They will face Czech Republic at the Estadio Azteca on Wednesday, while South Korea, on three points, face South Africa in Monterrey.