They have now gone eight World Cup matches without a win - going back to the group stages of 2010 - and face the daunting prospect of Germany in their final group game.
Group E concludes on Wednesday, when Mexico play Sweden in Ekaterinburg and Germany play South Korea in Kazan. It almost paid off after Hirving Lozano out-sprinted his marker, but his final delivery was blocked away.
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 unsafe. South Korea responded with fouls.
With South Korea's defence in disarray, Jang clearly handled Andres Guardado's cross and referee Mazic did not hesitate in awarding the penalty, Vela stepping up and sending Cho Hyun-woo the wrong way.
Mexico's ball control kept the South Korean side pinned to their half of the pitch until tactical changes took effect at the intermission.
Hernandez would not be denied again, though, the West Ham striker making no mistake in drilling in his landmark goal to send the raucous Mexican crowd into raptures.
Son Heung-min's stunning long-range effort in stoppage time gave South Korea a glimmer of hope but it was too little too late.
"We've beaten Germany and South Korea, two hard teams, but tomorrow we'll concentrate on thinking about Sweden".
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.
Just as South Korea were beginning to grow in confidence they fell behind.
It's the 50th career worldwide goal for Hernandez, known as "Chicharito".