Esteban Paredes and Arturo Vidal scored second-half goals for Chile, whose top scoring threats - Humberto Suazo and Alexis Sanchez - failed to break through but looked as dangerous as any players in the tournament.
In Monday's other Group C match, also played at San Juan, Luis Suarez scored in first-half stoppage time as Uruguay rallied for a 1-1 draw against Peru.
Chile and Uruguay meet on Friday in one of the best match-ups of the tournament.
Chile reached the second round in last year's World Cup - its best performance since 1962 - and Uruguay was the surprise semifinalist led by the tournament's top player, Diego Forlan.
All 12 teams have now played one match in the South American championship. Co-favorite Argentina managed only a struggling 1-1 draw with Bolivia, and Brazil was worse in a 0-0 draw with Venezuela.
“It's very even because there are good teams and great players,” Forlan said.
As good as Chile was, Mexico almost pulled off a stunning upset.
Nestor Araujo gave Mexico a 1-0 lead with a header in the 41st minute, a goal that came after Chile had dominated possession.
Mexico is playing with an understrength team - mainly youth players who were absent from the Mexico squad that defeated the United States 4-2 last month to win the Gold Cup in California.
Because it plays in the CONCACAF region, Mexico can only play in the South America tournament as a guest. It's fielding a youth team missing stars like Manchester's Javier Hernandez. Mexico was further weakened when eight players were kicked off the team for violating training rules after a friendly match last month in Ecuador.
“I think Chile is going to go a long way in this Copa America,” Mexico coach Luis Fernando Tena said. “This is the group stage, and from what I have seen of the 12 teams, I think Chile has played the best.” Tuesday is a rest day.
Argentina faces Colombia on Wednesday in the day's only game. Anything less than a lopsided victory and goals from Barcelona star Lionel Messi will turn up the heat on Argentina coach Sergio Batista, who took over from Diego Maradona following the World Cup.
Julio Grondona, president of the Argentina Football Association, has already placed the blame.
“Messi never plays badly,” Grondona said. “Those who play badly are those around him.” Batista is likely to make only one change for the match against Colombia, starting Pablo Zabaleta at right back to replace Marco Rojo. The rest of the team should remain the same with Messi, Carlos Tevez and Ezequiel Lavezzi in attack, supported by midfielders Esteban Cambiasso and Javier Mascherano.
“We're not going to go crazy because we didn't win the first match,” Batista said in a column Monday in the daily newspaper Clarin. “We know it's all just begun and we'll keep improving.” Tevez was in the headlines Monday after issuing a statement saying he wants to leave Manchester City.
He also handed in a transfer request in January but later withdrew it and helped City win the FA Cup and qualify for next season's Champions League. However, he seems unlikely to change his mind again after making it clear he wants to live in an environment where his wife Vanesa and their two daughters can feel at home.
Vanesa moved back to Argentina with the two girls after struggling to adapt to the English climate and culture.
“Living without my children in Manchester has been incredibly challenging for me,” Tevez said. “Everything I do, I do for my daughters, Katie and Florencia. I need to be closer to them and to spend more time with them. I need them to be happy because my life is about them now. I need to be in a place where they can adapt.” He did not say where he plans to move.
Manchester United winger Antonio Valencia missed practice for Ecuador on Monday with a left ankle injury, and coach Reinaldo Rueda suggested he may miss the team's next match in the Copa America against Venezuela.
Valencia left Sunday's match against Paraguay with the injury.
“For now, we can't count on him,” Rueda said. “We'll get more information later. We hope to have him, but we have to wait to see how serious it is.” Valencia broke his left ankle in September playing for Manchester United in a Champions League match, Enderwent surgery and was out for five months.
