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.
But despite seeing Mexico follow a 1-0 defeat of world champions Germany with another narrow win, Osorio was unhappy with the refereeing from Serbian official Milorad Mazic, who booked four Korea players. And all of them should be afraid of Mexico. A volley from Vela skimmed the bar minutes later. Son Heung-min pulled one back for South Korea in stoppage time with a spectacular left-foot strike from outside the area.
The closest they came to scoring in the first half was with a header from a corner which Mexico goalkeeper Guillermo Ochoa tipped over the bar.
But, six minutes before the half-hour mark, El Tricolor were handed the ideal opportunity to open the scoring when opposition defender Jang Hyun-soo needlessly went to the ground in an attempt to block an Andres Guardado cross - only to handle the ball inside the area.
The win puts Mexico in the driver's seat heading into their final match in the Group Stage.
The referee had no hesitation in awarding a penalty and, with similar conviction, Vela sent Cho Hyun-woo the wrong way from 12 yards to hand Mexico the lead.
Mexico relied on keeping possession and long-range shots, with a powerful attempt from Guardado forcing an athletic save from Jo in the second half.
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.
"We must prepare for the next game as if it is the last and get as far in the World Cup as we can".
Still, it proved to be little more than a mere consolation and Korea Republic will now need a favour from elsewhere if they are to have any chance of progressing to the knockout round.