Carlos Vela gave Mexico the lead with that penalty after Korean defender Jang Hyun-soo blocked Andres Guardado's cross with his arm inside the area, before the nation's all-time leading goalscorer Javier Hernandez doubled their lead in the second half with his 50th worldwide goal.
The result ended 2-1, giving Mexico two wins from two and putting them in the driving seat for top spot in Group F, and leaving South Korea without a win in two games and their World Cup hopes all but over.
Mexico will reach the last 16 should Sweden beat Germany in Saturday's final game, kicking-off at 19:00 BST. Coach Juan Carlos Osorio insisted that his team would not be complacent, however, underlining South Korea's tactical nous.
The game became more open in the second half as South Korea perhaps pushed too hard too soon, and it was little surprise when Mexico doubled their lead.
Mexico's all-time leading scorer was well marshalled by South Korea's defence for much of Saturday's clash in Rostov-on-Don, but took his chance when it came in the 66th minute, slotting home in composed fashion at the culmination of a wonderful counter-attack.
Mexico carried their momentum from an earthquake-inducing performance on Day One, to their fixture against two-time Asian Cup champs South Korea.
Mexico will qualify for the last 16 if they win and Germany fail to beat Sweden.
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The good news for South Korea was the early form of Son.
Just as South Korea were beginning to grow in confidence they fell behind. Carlos Vela made no mistake from the spot, sending Cho Hyun-woo the wrong way.
Vela then curled a shot high and wide after a quick break.
Mexico appeared in control but allowed the South Koreans to set up a nervy finale when Son struck a stunning goal from range three minutes into injury time.
South Korea wanted a penalty of their own after the restart when Moon Seon-min's strike clipped Carlos Salcedo's arm, but the referee correctly waved away their appeals.
Mexico had their second of the game in the 66th minute, however, when Hernandez collected a super pass from Lozano before finishing low into the bottom corner of the net to register his 50th worldwide goal.