Luis Suarez scored the winner in the 43rd minute after running unmarked to the back post and heading in Edinson Cavani's cross for his first goal of the tournament.
Mexico advanced to the round of 16 thanks to better goal difference than South Africa, which beat France 2-1.
Uruguay and Mexico went into the last group game sharing the lead on four points and needed only a draw to advance but they both fielded attacking lineups. Even so the game yielded few clear scoring chances.
"The important thing is that we qualified in first place," Uruguay striker Diego Forlan said. "They controlled the ball well and in truth it was quite hard for us." Uruguay, which didn't concede a goal in the first round, ended the group phase with seven points.
Mexico and South Africa both finished with four points.
Mexico coach Javier Aguirre preserved an attacking lineup that helped his team beat France 2-0 in its last game.
Veteran striker Cuauhtemoc Blanco, at 37 the oldest outfield player at the tournament, replaced the injured Carlos Vela as Mexico retained its 4-3-3 formation.
Uruguay coach Oscar Tabarez made just one change to the lineup that beat South Africa 3-0, bringing in defender Mauricio Vitorino for Diego Godin.
But the match was mostly subdued. Forlan, who scored twice and set up another goal against the host nation, never sparkled.
Suarez, a constant menace for the Mexican back line, first threatened in the sixth minute when he pounced on a long downfield pass which two Mexican defenders failed to stop and shot across the face of the goal.
Mexico's best chance came in the 22nd when Andres Guardado, who replaced suspended midfielder Efrain Juarez, fired a left-foot shot from 30 yards (meters) which bounced back off the underside of the crossbar.
Mexico went behind despite dominating possession, moving the ball easily around the pitch but failing to find holes in the Uruguay back line.
Mexico increased the pressure after the interval, and Blanco tested Fernando Muslera with a curling free kick the goalkeeper did well to hold.
But Diego Lugano almost extended Uruguay's lead with a close-range header that Oscar Perez couldn't hold and the Mexican defense bundled the ball out for a corner.
Francisco Rodriguez had Mexico's best chance to equalize in the 64th when he dived to meet a cross from substitute Pablo Barrera but his header glanced wide.
Substitute Javier Hernandez, who scored when he came on against France, almost connected in the 76th with the outside of his boot but opportunities were scarce for the Mexicans.
An unexpected late chance fell to Guillermo Franco after two Uruguayan defenders failed to stop a ball into the penalty area but the striker wasn't quick enough to take advantage.
Oscar Perez, Francisco Rodriguez, Carlos Salcido, Rafael Marquez, Ricardo Osorio, Geraldo Torrado, Guillermo Franco, Cuauhtemoc Blanco (Javier Hernandez, 63), Hector Moreno (Israel Castro, 57), Andres Guardado (Pablo Barrera, 46), Giovani Dos Santos.
Fernando Muslera, Mauricio Victorino, Diego Lugano, Jorge Fucile, Maximiliano Pereira, Egidio Arevalo Rios, Alvaro Pereira (Andres Scottie, 77), Diego Perez, Diego Forlan, Luis Suarez (Alvaro Fernandez, 85), Edinson Cavani.
