Captain Antonio Briseno set Mexico on its way on 31 minutes, top scorer Carlos Fierro flicking on a cross from the right for Briseno to volley home.
Uruguay twice came close to grabbing an equaliser, both Elbio Alvarez and Juan San Martin seeing efforts hit the post, but Mexico made sure of victory in the second minute of stoppage-time with Giovani Casillas grabbing his side's second.
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"This is an amazing feeling and one of my absolute greatest sporting moments here in Mexico," Mexico coach Raul Gutierrez told fifa.com afterwards.
"We have a strong group of players in this Mexican team. They behave well off the pitch and play with great spirit and technique when the whistle blows.
"They did absolutely everything I asked of them through the whole tournament and I couldn't be more proud of them."
Germany claimed third place after beating Brazil 4-3 in a thriller at Mexico City's Estadio Azteca.
