Vela and Hirving Lozano also had chances for Mexico, before the second goal arrived with 25 minutes to go through Mexican all-time top scorer Hernandez. If Germany fails to win, Mexico locks up a spot in the round of 16.
The forward scored from the spot in the 26th minute after defender Jang Hyun-soo handled the ball while sliding to block an Andres Guardado cross.
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.
The South Koreans had chances of their own through star striker Son Heung-min, but the Tottenham man was wasteful on several occasions - once when played through but allowing the Mexican defence to get back, and once seeing 'keeper Guillermo Ochoa save at his feet.
Mexico showed their quality on the break again when Miguel Layun fired in a cross that Lozano very almost got on the end of, but they did not have to wait much longer to take the lead.
Mexico carried their momentum from an earthquake-inducing performance on Day One, to their fixture against two-time Asian Cup champs South Korea. Chicharito's first goal in the competition was the insurance marker his team eventually needed to vanquish South Korea. A volley from Vela skimmed the bar minutes later.
South Korea's slim hopes of qualification hang on Germany beating Sweden and then losing to the Koreans themselves.
South Korea will face Germany at the same time in Kazan.
The goal was Hernandez's fourth strike at a World Cup and took him level with Luis Hernandez as Mexico's leading scorer in soccer's premier global tournament.
Mexico has reached the round of 16 in six straight World Cups, but the team has not advanced to the quarterfinals since playing at home in 1986.
- South Korea have conceded a goal via a penalty in both of their World Cup games so far in 2018 - in their previous 29 World Cup games combined, they only conceded one penalty goal.