Uruguay topped Group A with seven points
The result meant Uruguay topped Group A and Mexico also went through despite losing by virtue of having a better goal difference than hosts South Africa.
"We're going to take it one game at a time ... now we've been lucky enough to achieve our first goal which was to get through the group phase," said Uruguay's goalscorer Luis Suarez.
Image: Uruguay's Luis Suarez celebrates with team mate Diego Forlan after scoring against Mexico
A well-made and perfectly-taken headed goal by striker Suarez after 43 minutes settled the outcome of the match as Mexico lost their way after an evenly-balanced first half.
In a tightly contested, but open game, with no sign of any intention to play for a draw, Uruguay, champions in 1930 and 1950, had to resist Mexican pressure in the closing stages to keep a third straight clean sheet.
The first half was littered with stoppages, tension seeming to grip both teams.
As the sun went down, Mexico, playing the more intricate football, had the best early chance when Andres Guardado fired in a wicked left-foot drive from 30 metres that rebounded off the bar.
But Uruguay were in no mood to be dazzled or unnerved and, combining strength with pace in attack, they gave as good as they received in an evenly-balanced and, at times, fascinating contest.
Uruguayan midfielder Diego Perez suffered a cut head, apparently from an errant elbow, and required treatment before returning in a vivid blue bandage, just before his side swept ahead after 43 minutes.
Image: Uruguay's Diego Perez walks off the field after he was injured during a 2010 World Cup Group A soccer match against Mexico at Royal Bafokeng stadium in Rustenburg
