Carlos Tevez headed home controversially after 26 minutes from an offside position, before Gonzalo Higuain struck a second. Tevez hit a beautiful third in the second half before Javier Hernandez netted a consolation.
Mexico had two great chances early on to take the lead. First Carlos Salcido cut inside and unleashed a speculative effort from 35 yards out which had Sergio Romero had to flick onto the bar. Before the Albiceleste could draw breath, Giovani dos Santos made a break down the right before pulling the ball back for Jose Guardado, whose left foot shot from 20 yards swung just wide of the far post with Romero beaten.
Lionel Messi had a reasonably quiet opening, but played his part in the opener. He and Tevez ran in tandem at the heart of the Mexico defence and the Manchester City forward was able to squeeze the ball through for Messi to go one on one with Oscar Perez. After the keeper was able to foil him, Messi chipped the ball towards goal before Tevez, who was offside by at least a metre, headed home.
It momentarily appeared as though the strike was to be ruled out as referee Roberto Rosetti consulted his assistant at length, but despite protests from the Mexican players the goal was allowed to stand.
Within just seven minutes the Albiceleste rubbed salt into the open wounds by adding a second. Ricardo Osorio took his eye off a simple pass at the back and the loose ball was pounced upon by Higuain, who charged forward before coolly rounding Perez and slotting into the empty net.
It could so easily have been three after Messi’s throw was flicked on by Higuain and Tevez went on the rampage towards the Mexico goal, but el Tri managed to block his effort and then cleared Maxi Rodriguez’s cross soon after.
A further chance was wasted as Argentina really began to turn the screw. Otamendi did superbly to reach the bye-line before crossing for Higuain, who was unable to get enough contact onto his header and glanced wide from five yards.
After an initial period of cat and mouse at the start of the second half, the result was put beyond doubt by a moment of Argentine magic. Forced onto his left foot with seemingly nothing on, Tevez ducked back onto his right, getting a break off a Mexican defender as he did so, before unleashing an unstoppable effort from 25 yards.
To their credit, Mexico did not give up and, after heading wide, Hernandez got his name in spectacular fashion. He beautifully turned a static Martin Demichelis before firing a neat left foot finish high into the net at Romero’s near post.
There was one more opportunity for Mexico as a dangerous cross was swung over from the left, but Gabriel Heinze superbly flung himself at the ball to clear at the far post ahead of Marquez.
Messi could have finally got his World Cup account ticking in stoppage time when unleashing a superb left foot strike, but Perez did well to tip over. But it was too little too late for the keeper as Mexico crashed out.