Mexico laid one foot in the World Cup's last 16 and left South Korea on the brink of elimination after goals from Javier Hernandez and Carlos Vela clinched a 2-1 victory in Rostov on Saturday.
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.
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.
Mexico lead Group F on six points after two games, having backed up their shock victory against Germany with another display to suggest they can go deep in this tournament.
South Korea, beaten by Sweden in their first match, had their chances but again lacked cutting edge up front.
Yet to register a single point, they are left needing a miracle to progress.
OSORIO LIVID OVER FOULS
After the match, Mexico coach Osorio urged action against repetitive fouling after his team was on the receiving end of 24 fouls and South Korea received four yellow cards.
"Usually, I don't like to talk about referees but there was something I didn't like and that was that there were 24 fouls against us," said Osorio, whose own team committed seven fouls in the Group F match.
“It's very easy to analyse who committed them. For the good of football, I hope they take the necessary precautions and measures.”
Mexico, who have six points from two games and are on the brink of a last-16 place, began their campaign with a stunning 1-0 win over Germany but Osorio said it was important for his side not to get carried away by the euphoria.
"Since November, we have been developing a plan for regenerative work after matches," said the Colombian. "We must make sure the euphoria doesn't get the better of us and dedicate our efforts to recovering for the next game [against Sweden]."
Osorio, who is hoping to break Mexico's run of six successive round of 16 World Cup eliminations, said he spent a lot of time making sure complacency did not creep in after their win over Germany.
"What often happens against teams with less history is that the human being tends to relax but we dedicated all week to making sure we did not let that happen and fortunately the message didn't get lost among all the praise the team has received," he said.
He also paid tribute to their huge following of fans.
"It's very comforting and moving to see how the Mexican fans follow their team. I'm very moved listening to the national anthem, so imagine how the players feel," he added.
“I don't think there are many groups of supporters who show this unlimited passion for their team."
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