Having beaten Germany in their opening game, El Tri showed that it wasn't a fluke as Carlos Vela gave them the lead midway through the first half from the penalty spot.
Javier Hernandez then added a second goal in the 66th minute which was his 50th international goal which makes him Mexico's all-time top goalscorer.
South Korea did make things nervy at the end with a goal from Son Heung-min in injury time but at the end of the day they fell to a second successive defeat in Group F which all but ends their World Cup dream.
Korea made a bright start but failed to take their chances
Given their respective results in their opening games, it was only natural that it took this game a little bit of time to get going but when it did, both sides started to create chances at will.
It was the Koreans, though, who had the first big chance of the game when a great passing move ended with Hwang Hee-chan crossing the ball into the path of Lee Yong.
He was about the volley the ball into the back of the net but Hirving Lozano, knowing for his attacking skills, tracked his man all the way into his own box and threw himself at the ball to block the goal-bound effort.
Soon after this chance, Ki Sung-yueng came close to scoring as well for the Koreans but he saw his goalbound header well-saved by the impresisve Guillermo Ochoa.
Vela opened the scoring for El Tri from the penalty spot as Korea remained frustrated
Them chances seemed to spark Mexico into life and they took the lead in the 26th minute of the game from the penalty spot after referee Milorad Mažić pointed to the spot after Jang-Sang-won handled Andrés Guardado's cross into the box.
Vela stepped up to take the spot kick and calmly slotted the ball into the back of the net sending the keeper the wrong way.
El Tri had their tails up after taking the lead and they almost made it 2-0 soon after with Miguel Layún seeing his shot from the edge of the box well-saved by Jo Hyeon-Woo.
It was end to end action for the remainder of the first half as Lozano and Son both had chances for their respective sides before the break but failed to hit the target as Mexico took a slender lead into the break.
Hernandez netted his 50th goal for El Tri becoming their all-time top goalscorer
The end to end action continued on at the start of the second half as Mexico almost doubled their lead 10 minutes after the break when a shot from Guardado was heading into the top corner of the net but for a brilliant save from Hyeon-Woo.
El Tri did make it 2-0, though, in the 66th minute when a great run from Lozano resulted in the winger playing Hernandez through on goal and the striker remained calm and slotted the ball into the back of the net to make history for his country by becoming their all-time top goalscorer.
After doubling their lead though Mexico took their foot off the pedal and that allowed the Koreans to get back into the game but they found the Mexican defence to be very stubborn to break down.
Son's late strike not enough for Korea as El Tri held on
That was until the third minute of injury time when Son picked up the ball along way outside the box and unleashed a fantastic left-footed strike which flew into the back of the net leaving Ochoa with no chance.
The goal though came to late as the Mexicans held on for their second consecutive victory in Group F, while the Koreans fell to a second defeat and are all but out of the competition with one game to go in the group stage.