Bolivia hit the post through Ricardo Pedriel with their first real attack, and Mexican stiker Raul Jimenez should have scored after the break with a close range header, but otherwise neither side created much in the way of clear-cut chances.
The Mexicans also had a penalty appeal turned down late on after Javier Aquino went down under pressure from Alejandro Pinedo.
While on balance a draw looked to be a fair result, it was greeted by whistles and boos at the Sausalito stadium in Vina del Mar at the final whistle.
Mexico have never defeated Bolivia at the Copa America in three attempts, though they have beaten them in each of their nine encounters in other competitions and friendlies.
The Mexicans now face Chile in Santiago on Monday while Bolivia meet Ecuador in Valparaiso on the same day.
Chile beat Ecuador 2-0 in the tournament opener on Thursday.
“We know that Chile are coming off the back of a victory that will give them a bit of confidence, and they have some quality players, but so do we, and we’re going to work hard to beat them,” Mexico striker Jesus Corona said.
After two slightly disappointing matches on the opening two days, the Copa is expected to come to life over the weekend when favourites Brazil and Argentina, along with defending champions Uruguay, all open their accounts.
Uruguay face Jamaica in Antofagasta on Saturday, Argentina take on Paraguay in La Serena the same day and Brazil meet Peru in Temuco on Sunday.
(Editing by Peter Rutherford)
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