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.
It's the 50th career worldwide goal for Hernandez, known as "Chicharito".
The hapless Koreans, who have no points after two matches and have only won one of their last 11 World Cup fixtures, can still theoretically qualify for the next round but they need to beat Germany and hope Mexico win against Sweden. It gives rhythm to Mexico's attacking.
Meanwhile, while the South Koreans are not mathematically out of it - at least until the game between Germany and Sweden later on Saturday - it will take a minor miracle if they are to have any chances of keeping their World Cup dream alive.
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.
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Her opening partner Katherine Brunt was slightly less parsimonious, but made up with two wickets, finishing with 2/18. The Brits were all blazing guns with Tammy Beaumont's 116 runs off 52.
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She's spoken with him three times , for five minutes each, since the separation more than a month ago. The man said he worries about his son, who speaks only Portuguese.
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South Korea will face Germany at the same time in Kazan.
Edson Alvarez was brought in as centre back for Mexico's World Cup Group F game against South Korea on Saturday in the only change made by coach Jose Luis Osorio after the Latin Americans defeated defending champions Germany.
El Tri's form, confidence and collective spirit in Russian Federation surprised everyone in its World Cup opener, and Juan Carlos Osorio's team won't pass up the chance to announce itself as Group F's team to beat when it faces South Korea.
Son, the team's star player, was left with too much to do up front.
Mexico so far is one of the teams that has a ideal run in the campaign and has conceded just one goa. It looked like it could possibly work in moments, but this South Korea side needed to provide more against a Mexican collective that is really clicking and not reliant on any one individual.
Korea's talismanic forward Son Heung-min struck a scorching consolation goal in stoppage time from outside the area. South Korea lost its opening match.