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Despite the defeat, the Mexicans also progressed, having edged hosts South Africa out of the runners-up spot on goal difference.
Suarez’s header just before half-time settled a full-blooded contest which belied fears that the two sides — who kicked off knowing a draw would see both of them through — would decline to make a fight of it.
“The important thing was to win and finish top of the group,” said Uruguay striker Diego Forlan.
Mexico defender Rafael Marquez said his side needs to improve for the second round where their opponents could be Argentina.
“We will have to improve. As for (now likely meeting) Argentina, we will have to work to reproduce the kind of form we showed in the match against France,” said the Barcelona star.
Uruguay were superior throughout and, with better finishing, would have won more comfortably, although Mexico also had their moments, notably when Andres Guardoado’s wonderful strike crashed against the bar midway through the opening period.
A feisty opening period might easily have ended with Uruguay building up the kind of lead that would have given South Africa, 2-1 winners over troubled France in their final match, hope of snatching second place.
They should have taken a sixth minute lead after a fluffed clearance by Hector Moreno left Suarez with only Mexican goalkeeper Oscar Perez to beat but the forward dragged his shot from the right of the goalmouth beyond the far post.
Another chance for Uruguay went begging in the 19th minute when Mauricio Victorino headed Diego Forlan’s corner over the bar from an unmarked position on the edge of the six-yard box.
The Uruguayans were bossing the game but Mexico came agonisingly close to opening the scoring when Guardado, in for the suspended Erwain Juarez, struck the under-side of the bar with a swerving left foot drive from 30 yards out.
Giovani Dos Santos then wriggled clear inside the area but Porto defender Jorge Fucile recovered with a superb last-ditch tackle to snuff out the danger.
Uruguay finally took the lead two minutes before the interval when Edinson Cavani got free on the right. His delivery to the back post was impeccable and Suarez peeled away from his marker to nod the ball past Perez.
Uruguay’s tempo eased off after the interval but it required a superb stop from Perez to prevent them doubling their lead as the hour mark approached.
Uruguayan skipper Diego Lugano rose above the Mexican defence to power Forlan’s free-kick goalwards and the goalkeeper had to throw himself full length to save.
Mexico’s clearest chance of the afternoon followed ten minutes later. Substitute Pablo Barrera’s cross found Francisco Rodriguez unmarked on the six-yard line but the defender failed to connect cleanly and his header slipped wide of the target in what was to prove Mexico’s last chance of an equaliser.
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