Javier Hernández scored the second after 66 minutes, finishing off a rapid break.
Carlos Vela scored in the first half on a penalty kick and Javier Hernandez doubled the score with a fine finish in the second half, as El Tri built off the win over Germany with another crucial victory that puts them a step closer to the round of 16.
Hernandez added the second in the 66th, scoring his 50th goal for Mexico.
The South Koreans managed successive counterattacks by targeting striker Son Heung-min but caused few problems for Mexican goalkeeper Guillermo Ochoa.
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Lozano and Vela then took it in turns to try their luck, but the former saw his goal-bound effort blocked before the latter curled over the crossbar during an open period of the match.
Mexico's win keeps them top of Group F on six points and leaves the Germans facing the growing possibility of a last-16 clash with five-times winners Brazil. Defender Edson Alvarez replaced Hugo Ayala at the back.
If Germany lose to Sweden in the evening's Group F game at the Fisht Stadium in Sochi then Joachim Löw's side will be out. This win followed one of the World Cup's most confounding upsets, when Mexico toppled Germany 1-0 in its opener.
The 20-year-old Alvarez, one of Mexico's hottest prospects, replaces Hugo Ayala.
Mexico nearly doubled their lead one minute later when Layun unleashed a powerful strike from inside the South Korea box, but Cho Hyun-woo was on hand to make an excellent save.
Mexico can qualify for the knockout phase if Germany fail to beat Sweden later today.