This win followed one of the World Cup's most confounding upsets, when Mexico toppled Germany 1-0 in its opener.
South Korea coach Shin Tae-yong stuck to his attacking line up but shook up his midfield with Ju Se-jong and Moon Seon-min coming in for Park Joo-ho and Koo Ja-cheol, as the 2002 semifinalists seek to recover from their opening 1-0 loss to Sweden. Carlos Vela sent Jo the wrong way for the first goal of the game. South Korea's lone goal, in extra time, came too late and Mexico won 2-1.
Mexico dominated possession throughout the match, striking first blood in the 26th minute from the penalty area, when Carlos Vela cooly converted his spot kick.
Miguel Layun pressed for a second goal before the break but his shot from a low cross-field drive was tipped away by Jo Hyeon-woo. "They tend to relax, they tend to lose focus, so every weekend, every match, we insist on being fully focused on not losing that important message", Osorio said. Heung-Min Son scored in the stoppage time to half the deficit but in the end it was no more than a consolation.More news: Dont blame Messi, pleads Argentina boss Sampaoli
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The South Koreans, who have lost their opening two matches, kept Ochoa under pressure throughout the match with Son often out-sprinting the Mexican defense.
Ki Sung-yueng threatened in the 56th minute with a ferocious drive that Guillermo Ochoa could only gather at the second attempt, before Cho did well two minutes later to keep out a curler by Guardado at full stretch.
Carlos Vela got the Mexicans on their way at the Rostov Arena with a 26th-minute penalty, before Javier Hernandez wrapped up the three points with a second six minutes after the hour mark.
Mexico has reached the round of 16 in six straight World Cups, but the team has not advanced to the quarterfinals since playing at home in 1986.
Mexico is now assured of a slot in the round of 16 and now joins hosts Russian Federation and Uruguay from Group A, France of Group B and Croatia in Group and Croatia of Group C. Mexico unsurprisingly overcame Germany in their opening game.