Mexico left back Jesus Gallardo received a yellow card for elbowing Sweden's Ola Toivonen just 13 seconds into the match, the quickest a player has ever been booked in the World Cup.
Second-half goals from defenders Ludwig Augustinsson and Andreas Granqvist, from the penalty spot, plus a comical own goal were reward for a physical display from Sweden, who only made it to Russian Federation by beating Italy in the play-offs.
With the game fading into injury time and Sweden certain of victory, Mexican fans began to think what was before the game unthinkable - possible elimination.
Mexico has had an excellent start to the 2018 World Cup but still has a chance to make history in an unwanted way.
El Tri will now play the victor of group E which, depending on results in the two matches to be played later today, could be Brazil, Switzerland or Serbia.
Sweden must win in order to make sure of a second round spot.
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When Edson Alvarez got his legs tangled and turned the ball into his own net, the writing was on the wall for Mexico.
If Mexico beats Sweden on Wednesday it would win its group with a flawless record, something it has never achieved in its long World Cup history. The Germans came into the match knowing that a win by two goals would have been enough to advance.
"We hadn't done any sort of mathematical calculations", Ochoa said at a news conference. His status for Monday's Round of 16 match with Mexico is unclear.
The drama kept on coming as Javier "Chicharito" Hernandez looked to have handled the ball in the box and referee Nestor Pitana used VAR to check the incident but stuck with his initial decision of no penalty.
Sweden thrashed Mexico in the second half take control of the group, and Juan Carlos Osorio's side failed to create many legitimate scoring chances.
It took them less than 30 seconds to make their mark on Sweden, Jesus Gallardo earning a yellow card for clattering into Ola Toivonen nearly straight from kick-off. The Swedes stayed crisp in their exchanges and it helped them find seams in El Tri's defence. Costly mistakes enlarged the score, and at the 90th minute, Sweden walked away with a 3-0 victory. And there is a strong belief within the team that they can beat Mexico.