Mexico are in full control of Group F while South Korea will need to look ahead to their final match of the round against Germany with slim hopes of making it through to the knock out stages.
Goals from former Arsenal forward Carlos Vela and West Ham's Javier Hernandez were enough for the side that shocked the reigning world champions in their opening encounter of the World Cup 2018.
A rocket from Son Heung-min raised hopes of a late South Korean comeback but it was not to be. They were second best to Mexico all over the pitch for most of the game.
South Korea
Goalkeeper: Cho Hyun-Woo
Was his team's top performer despite seeing two goals hit he back of his net. Made good saves to deny Andres Guardado and Hirving Lozano. 7
Right-back: Lee Yong
Put in some good challenges, especially around his own box, but was overrun in the end. 6
Centre-back: Jang Hyun-Soo
Blamed for injuring a teammate in his side's opening game against Sweden, he gave away the penalty for Carlos Vela to score. A poor tournament so far. 3
Centre-back: Kim Young-Gwon
Did what he could to hold back his opponents, and made some big interventions inside his own half. Couldn't hold the line by himself. 7
Right-back: Kim Min-Woo
A stable performance down the right from South Korea's other full-back, Kim also found Mexico to be too much as they surged down the flanks. Taken off late in the game. 6
Midfield: Ju Se-Jong
Taken off early in the second half to make way for Lee Seung-woo. South Korea looked better with his replacement on the field as they began to play with a more positive outlook. 4
Midfield: Ki Sung-yueng
Found himself up against a tenacious opponent in Hector Herrera but was able to give South Korean some security on the ball, if not quite victory in the control over the midfield battle. 6
Right wing: Moon Seon-Min
Simply second best down his side of the pitch against Mexico's pairing of Hirving Lozano and Jesus Gallardo. Taken off in the second half after a tough shift on the right. 5
Attacking midfield: Lee Jae-Sung
Played all over the pitch in a rugged performance that saw him moved around to fight fires caused by South Korea's problematic match ups in the individual battles against Mexico. 7
Left wing: Hwang Hee-Chan
A similar outing to Lee, Hwang was one of South Korea's better performers against a very dangerous opponent. Unlike some of his countrymen he at least looked worthy of being on the pitch alongside some of the bigger names on either team. 6
Striker: Son Heung-Min
Clearly his side's best chance of scoring but the Spurs forward had too much to do and seemed determined to take on the burden himself, rather than trust in those around him. Understandable but he was still ineffective - until that cracker of a goal in injury time of course! 5
Mexico
Goalkeeper: Guillermo Ochoa
Another solid performance from the shot-stopper who denied Germany. Had less to do that in that game but still alert to dangers as they cropped up. Beaten only by a stunner from Son. 7
Right-back: Edson Alvarez
The weak spot in the Mexican back line, he was fortunate to have Miguel Layun ahaed of him working hard to help keep his side of the pitch covered and under control. 4
Centre-back: Carlos Salcedo
Started well but looked shaky at times in the second half and was sloppy on the ball. Made up for it with his commitment to throwing his body in the way of danger, although better sides are likely to take advantage of any further lapses from the defender. 5
Centre-back: Hector Moreno
Had an iffy second half, like his partner at the back, as South Korea sort to force the Mexican lock after failing to pick it throughout the opening 60 minutes, but was the more composed centre-back. 6
Left-back: Jesus Gallardo
One of the players who set the tone for the team from back to front. Helped to unleash his team's forwards and track back South Korea's goal threats down his flank. 7