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.
Hernandez's 50th goal for Mexico proved to be the match-winner.
Korea's talismanic forward Son Heung-min struck a scorching consolation goal in stoppage time from outside the area.
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.
Hernandez also scored for Mexico on June 23 at the last World Cup, netting in a 3-1 defeat of Croatia.
Carlos Vela put them ahead from the penalty spot in the 26th minute at Rostov Arena, which had been taken over by Mexico's sea of fanatical supporters.
Only a Germany win will prevent South Korea being knocked out with a group game remaining. The Mexicans were awarded the penalty after Jang Hyun-soo handled the ball while trying to stop a cross from Andres Guardado.
Osorio's team started on the front foot, with Miguel Layun seeing plenty of the ball in wide positions. A volley from Vela skimmed the bar minutes later.
After countless efforts to get a breakthrough, Tottenham Hotspur striker Son was finally rewarded as he curled home an audacious strike from outside the box two minutes into added time to make it 2-1. He hit the ball low past goalkeeper Jo Hyeon-woo after collecting a pass from Hirving Lozano.
Mexico will reach the last 16 should Sweden beat Germany in Saturday's final game, kicking-off at 19:00 BST.
Ki Sung-yueng threatened in the 56th minute with a ferocious drive that Guillermo Ochoa could only gather at the second attempt, before Cho did well two minutes later to keep out a curler by Guardado at full stretch.
Even if Germany wins, it would still be extremely unlikely that El Tri would not qualify for the second round of the World Cup for the seventh consecutive time.