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.
Giovani Dos Santos; Hector Herrera; Jesus Gallardo and Jesus Corona of Mexico celebrate after winning against South Korea.
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.
With the second goal Mexico tried to shut up shop by sending on the experienced Rafael Marquez for Guardado.
At face value, it would appear that Mexico are going to run roughshod over South Korea.
The South Koreans managed successive counterattacks by targeting striker Son Heung-min but caused few problems for Mexican goalkeeper Guillermo Ochoa.
South Korea lost their opener, falling 1-0 to Sweden in Nizhny Novgorod.
If Germany fails to win, Mexico locks up a spot in the round of 16.
Conditioned by the dry heat that has been a feature of every game at the Rostov Arena, Mexico did not quite have the same thrust and energy as against Germany although they still controlled most of the play and looked far more risky.
The 20-year-old Alvarez, one of Mexico's hottest prospects, replaces Hugo Ayala.
Leading Group F on six points from two games, Mexico will be assured of a place in the knockout stage if Germany draw or lose against Sweden. Carlos Vela sent Jo the wrong way for the first goal of the game.