Mexico were looking to build on their famous victory over the defending champions Germany in the group opener and, after a slow start this weekend, Javier Hernandez headed wide from a free-kick by Hector Moreno.
Son Heung-min broke free down the right after beating the offside trap, but his cut-back into the box to take a shot was blocked by not one but three bodies.
Korea was on the ascendancy momentarily and a header from Kim Young-gwon was expertly tipped over by Guillermo Ochoa.
Mexico were awarded a penalty when Jang Hyun-soo handled a cross from Andres Guardado after 23 minutes. Carlos Vela sent Jo the wrong way for the first goal of the game.
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.
Mexico staved off an early onslaught after the Koreans threw a number of bodies forward in an effort to get the equaliser.
However, that left them exposed at the back, where El Tri pounced on the counterattack on a few occasions. It nearly paid off after Hirving Lozano out-sprinted his marker, but his final delivery was blocked away.
At the midway point, the masterstroke finally paid dividends as a long ball made contact with Hernandez, who side-stepped two defenders before firing a low finish past Jo.
After countless efforts to get a breakthrough, Tottenham Hotspur striker Son was finally rewarded as he curled home an audacious strike from outside the box two minutes into added time to make it 2-1.
However, it was not enough for the South Koreans as Mexico and Juan Carlos Osorio bagged all the points.