Mexico took the lead in the 26th minute from the penalty spot, after Jang Hyun-soo was penalised for handball when he went to ground to intercept a cross. Heung-Min Son scored in the stoppage time to half the deficit but in the end it was no more than a consolation.
Mexico lead with six points from two games while South Korea have lost both matches and have only a remote mathematical chance of progressing.
It's the 50th career global goal for Hernandez, known as "Chicharito".
The win also piles the pressure on Germany as they prepare to face Sweden later today in Sochi, after the reigning champions' opening game defeat and the Swedes' opening victory over South Korea.
Mexico is in almost complete control over South Korea at halftime at the World Cup despite just a 1-0 lead courtesy of a Carlos Vela penalty kick.More news: Half of Aquarius rescue boat migrants want to seek asylum in France
South Korea threatened again nine minutes later, Son breaking clear of Mexico's line before letting rip with a low drive that Hector Moreno did well to keep out.
"But as of tomorrow we will be working hard thinking about Sweden and regardless of the results of the matches against Germany and South Korea, we are going to go out there to get the three points".
Javier Hernandez and Miguel Layun of Mexico celebrate their team's victory in the World Cup match against South Korea on June 23, 2018, in Russian Federation.
Mexico have taken a huge step towards the last-16 stage of the 2018 World Cup courtesy of a 2-1 win over South Korea in Rostov.
Carlos Vela stepped up to slot the ball home, sending South Korean goalkeeper Cho Hyun-Woo the wrong way from what was the 14th penalty in 28 games at Russian Federation 2018.