Pre-match predictions suggested that the two teams would be content to play out the draw which would guarantee them both a place in the knockout stages - and eliminate South Africa and France.
But Suarez headed home Edinson Cavani's right-wing cross on the stroke of half-time to settle the match.
The result meant that Mexico progressed on goal difference, while unbeaten Uruguay qualified top with seven points having still to concede.
Group A Standings
Group A W D L F A GD Pts Uruguay 2-1-0 4:0 +4 7 Mexico 1-1-1 3:2 +1 4 South Africa 1-1-1 3:5 -2 4 France 0-1-2 1:4 -3 1