The victory meant Mexico laid one foot in the Round of 16 and left Korea Republic on the brink of elimination after goals from Javier Hernandez and Carlos Vela clinched the Mexicans the win.
Hernandez became the first Mexican player to score 50 goals for his country, after 104 appearances, with Vela earlier opening the scoring through yet another penalty kick.
Son Heung-min's stunning long-range effort in stoppage time gave Korea Republic a glimmer of hope but it was too little too late.
Mexico lead Group F on six points after two games, having backed up their shock victory against Germany with another display to suggest they can go deep in this tournament.
Korea Republic, beaten by a Sweden penalty in their first match, had their chances but again lacked cutting edge up front.
With Germany beating Sweden 2-1 in the group's other match, the Taeguk Warriors still have a mathematical chance of progressing provided they beat the defending champions in their last match on Wednesday and Mexico defeat Sweden. Even if that happens, goal difference will be the decider.
After 28 games at the World Cup, there have now been 14 spot-kicks, 11 of them converted, and there could be little complaint about this one, coming after a blatant handball by Jang Hyun-soo, Vela stepping up to convert.
In temperatures around 35 degrees Celsius, Mexico were rewarded for another controlled performance that combined possession in midfield with pace and penetration in attack. Hirving Lozano, the match-winner against Germany, was excellent again in particular.
Before their opening goal, however, it was Korea Republic who created the better chances.
Only a brilliant saving tackle from Lozano denied Lee Yong tapping in at the back post before Son saw three quick-fire shots come to nothing, the first two blocked, the last skewed wide.
But Mexico's penalty in the 27th minute was clear. Jang tried to block Andres Guardado's cross but inexplicably slid with his arm outstretched above him and the ball struck the defender's hand.
Vela was made to wait by goalkeeper Jo Hyeon-woo, who played for time by swigging his water and chatting to his teammates, but there was no mistake. Vela slid home.
The game became more open in the second half as Korea Republic perhaps pushed too hard too soon, and it was little surprise when Mexico doubled their lead.
They were fortunate not to concede a foul for a clear trip by Hector Herrera in the build-up but Lozano found Hernandez and the striker did the rest. The former Manchester United striker's dummy-shot fooled the lunging Jang before a scuffed finish rolled past Jo.
Son should have capitalised on a Rafael Marquez mistake late on but made amends in the 93rd minute with a fabulous effort that soared into the corner. Mexico, however, held on.
Sources: AFP, FIFA via Getty Images
