Rafael Marquez, Andres Guardado and Javier Hernandez scored in a 10-minute span in the second half, dooming a talented Croatia side to elimination from the group stage.
The Croats had to win to advance and held the bulk of possession, but had trouble seriously threatening goalkeeper Guillermo Ochoa, who kept out all efforts until an 87th-minute consolation goal from Ivan Perisic.
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Mexico entered the game needing only a draw, and looked dangerous in attack, but was kept out until the 72nd minute.