In total contrast, Chile midfielder Manuel Iturra was sent off on the hour for his second red card in five days having been dismissed on Wednesday playing for Universidad de Chile in the Libertadores Cup.
Medina, who scored in last week's 1-0 win over Senegal in Chicago, took a pass from Cuauhtemoc Blanco on the edge of the box and fired home a left-footed shot for the only goal in the 14th minute.
Striker Javier Hernandez could have increased Mexico's lead but his shot two minutes after Iturra's dismissal hit the post.
Substitute Iturra had only been on the pitch one minute when he was sent off for a foul from behind on midfielder Andres Guardado.
Chile, who travelled to Mexico without Humberto Suazo and Esteban Paredes who are recovering from injuries, began the match with no recognised strikers in their line-up.
Mexico have won their last three warm-up matches 1-0. They beat Angola 1-0 with a Guardado goal in Houston on Thursday.
Coach Javier Aguirre dropped two defenders, Juan Carlos Valenzuela and Adrian Aldrete, from his squad before the match.
He now takes the remaining 24 players on a tour of Europe where Mexico will meet England on May 24, Netherlands on May 26, Gambia on May 30 and Italy on June 3. He will trim his squad to 23 for the finals by June 1.
Mexico meet hosts South Africa in the opening match of the World Cup. They also face Uruguay and France in Group A.
Chile face Honduras, Switzerland and Spain in Group H.
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