Mexico booked a last-16 tie against the Netherlands after knocking Croatia out of the 2014 Fifa World Cup.
The Croats, who knew a win would put them through, survived a scare when a Hector Herrera strike hit the crossbar.
But Rafael Marquez headed in for Mexico before Andres Guardado drove in a shot and Javier Hernandez nodded home to put them 3-0 up.
Ivan Perisic scored for Croatia, whose misery was compounded when Ante Rebic was sent off late on.
It was an accomplished display from the North Americans, who nullified Croatia’s threat before imposing their authority on the game.
A draw would have been enough for Mexico, but they made sure of a seventh knockout stage appearance in the last eight tournaments with a victory.
In contrast, Croatia crumbled in the latter stages and have now been eliminated at the group stage in four of their last five major tournaments.
Croatia playmaker Luka Modric had claimed Mexico benefited from a “great deal of luck” in their draw with hosts Brazil, but it was the Real Madrid midfielder’s side who enjoyed the early fortune at the Arena Pernambuco in Recife.