Hernandez added the second in the 66th minute, cutting inside his marker before guiding the ball home to finish off a lightning counter-attack after Mexico won the ball deep in their own half.
ROSTOV-ON-DON, Russia-There were plenty of teams to be afraid of at the start of this World Cup.
Hernandez became the first Mexican player to score 50 goals for his country, after 104 appearances, with Vela earlier opening the scoring through yet another penalty kick. Led by Tottenham's Son Heung-min, South Korea can't be overlooked by a Mexico side that has big goals following its statement victory.
With the second goal Mexico tried to shut up shop by sending on the experienced Rafael Marquez for Guardado.
Mexico have three points, while South Korea have zero after losing 1-0 to Sweden in their first match.
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.
Mexico were awarded a penalty when Jang Hyun-soo handled a cross from Andres Guardado after 23 minutes.
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South Korea lost their opener, falling 1-0 to Sweden in Nizhny Novgorod.
The win puts Mexico in the driver's seat heading into their final match in the Group Stage.
- In the first half, Son Heung-min had six shots (including blocked attempts) - more than South Korea managed in the entirety of their first match against Sweden.
Mexico had their second of the game in the 66th minute, however, when Hernandez collected a super pass from Lozano before finishing low into the bottom corner of the net to register his 50th worldwide goal.
The 20-year-old Alvarez, one of Mexico's hottest prospects, replaces Hugo Ayala. Look for Lozano and Chicharito to challenge South Korean goalkeeper Cho Hyun-woo throughout Saturday's concluding match, and the rest of the Mexican team will get in on the attack as well.
Having upset defending champions Germany in their opening game in Group F, Mexico proved again they will be a test for any side should they reach the knockout stages.