Mexico captain Rafael Marquez led by example thumping in a second-half header to set his country on the way to a place in the World Cup's last 16, knocking out ten-man Croatia in the process.
With both teams having a chance of qualifying ahead of their encounter, the first half proved an engaging affair although it was Mexico who provided the biggest threat with Hector Herrera striking the bar.
And with Croatia fading after the break, the Mexicans came strong with Marquez, who has so far marshalled a back line which has conceded just once all tournament, headed in on 72 minutes.
Andres Guardado and Manchester United's Javier Hernandez then added two more goals as Mexico, who finished second in group A behind hosts Brazil after their win over Cameroon, set up a second-round clash with the Netherlands despite Ivan Perisic's consolation for Croatia.
With four points from their opening two games against Cameroon and Brazil, the Mexicans were in the driving seat before kick off, knowing a draw would be enough to see them progress.
Croatia meanwhile needed maximum points at the Arena Pernambuco in Recife and went on the attack early, winning a series of early corner which came to nothing.
Croatian Ivan Rakitic became the first man to go into referee Ravsham Irmatov's book as he scythed down the advancing Jose Juan Vazquez on nine minutes.
While the first opening arrived four minutes later when Croatia broke at speed and Perisic crossed from the right but Ivica Olic was unable to time his arrival into the box in time.
It was then the turn for Mexico to attack as Herrera picked up the ball and fired in a scorcher from 30 yards but it rebounded back off the bar with Stipe Pletikosa stranded.
Miguel Herrera's Mexico were starting to find their feet but the head coach was left with his head in his hands as Oribe Peralta slipped at the vital moment when free in the box and his shot skied over the bar.
But Croatia were looking dangerous on the attack and Marquez also picked up a yellow card after stopping Peresic in their tracks – the niggling fouls certainly picking up as half-time arrived.
It was Croatia who started the half brightly, with former Tottenham midfielder Luka Modric – a peripheral figure in the first half – driving from deep before the ball was eventually deflected out for a corner.
With the game ticking past the hour, Mexico thought they should have had a penalty when Darijo Srna handled Guardado's shot in the box and then saw Croatia's Vedran Corluka clear off the line.
But they finally got the breakthrough as Marquez headed Herrera's centre past Pletikosa before a quick break shortly afterwards resulted in Guardado side footing home.
And after Croatian substitute Ante Rebic saw his effort cleared off the line by Hector Moreno, Hernandez nodded in from close range for a third.
There was still time for Croatia to ruin Mexico's unblemished defensive record as Perisic scored a consolation but already heading out of the tournament, substitute Rebic ended things on an even worse note after seeing red for a dangerous tackle.
Croatia 1
Perisic 87
Mexico 3
Marquez 72
Guardado 75
Hernandez 82
Referee: Ravshan Irmatov
Attendance: 41,212
Croatia: (4-2-3-1) Pletikosa, Srna, Corluka, Lovren, Vrsaljko (Kovacic 58), Rakitic, Pranjic (Jelavic 74), Perisic, Modric, Olic (Rebic 69), Mandzukic
Subs not used: Zelenika, Vukojevic, Schildenfeld, Brozovic, Badelj, Sammir, Vida, Eduardo, Subasic
Mexico: (5-3-2) Ochoa, Aguilar, Rodríguez, Márquez, Moreno, Layun, Herrera, Vazquez, Guardado (Fabian 84) dos Santos (Hernandez 62), Peralta (Pena 79)
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