The result was disappointing for Mexico, which is playing what amounts to its B team but was still a favorite to beat Bolivia, which has not won a match in this tournament since 1997.
Mexico’s best players like Carlos Vela and Javier Hernandez are being held out for next month’s Gold Cup in the United States.
“We came here look for a result,” Mexico coach Miguel Herrera said. “We tried, but we lacked consistency, and we are very aware of this.”
Bolivia had clear scoring chances, particularly in the first half, while Mexico’s best opportunity came early in the second half when substitute Raul Jimenez headed just wide in the Group A match.
Mexico defender Rafael Marquez, playing his fifth Copa America, went off early in the second half with an apparent injury.
“We have to wait for the doctor’s result, but he felt something in his left leg,” Herrera explained. “I didn’t want to risk it so I took him out.”
Bolivia had three good chances to take the lead.
Ricardo Pedriel hit the post in the 15th minute. Mexico goalkeeper Jesus Corona made a leaping save in the 42nd on Jhasmani Campos’ rising shot, and seconds later Ronald Raldes headed a ball just wide.
“We’re satisfied with the way we worked,” Bolivia coach Mauricio Soria said. “I hope this result gives us the respect we deserve.”
Mexico had a more of the ball in the second, but Bolivia looked better on the counterattack. Mexico pressed for the last 10 minutes and came close to breaking through several times.
Chile defeated Ecuador 2-0 on Thursday in the tournament and Group A opener.
In their next matches Monday, Mexico plays Chile and Ecuador faces Bolivia.