The victory thrilled a boisterous crowd at Azteca Stadium in Mexico, which is getting used to football success. Two weeks ago the Mexico senior team won the Gold Cup regional championship, defeating the United States 4-2 in the final in California.
Mexico also won the Under-17 world title in 2005. Nigeria has won this championship four times, and Brazil has won three.
Briseno scored chipping in a short shot from a header into the area, beating keeper Jonathan Cubero. Casillas got his two minutes into stoppage time, scoring on a counterattack as Uruguay pressed for an equalizer.
Uruguay had its chances with Elbio Alvarez hitting the crossbar.
Germany defeated Brazil 4-3 in Sunday's playoff for third place.