Miguel Layun's 18th-minute strike was the difference as Mexico emerged victorious at Dick's Sporting Goods Park.
While the win ensured Mexico left the United States unbeaten after Saturday's goalless draw against Chile, it heaped further misery on Bolivia.
Bolivia, who finished second-bottom in the CONMEBOL section of World Cup qualifying, have not won a game since they edged Haiti 2-1 in February last year.
The likes of goalkeeper Daniel Vaca, Daniel Chavez, Danny Bejarano and Leandro Maygua were promoted to Bolivia's line-up as coach Xabier Azkargorta went in search of a response following Saturday's 4-0 rout to Ecuador.
Mexico coach Miguel Herrera named a completely different starting XI to the one that faced Chile on the weekend, with Layun, Moises Munoz, Hugo Ayala, Hiram Mier, Marco Fabian, Javier Aquino, Antonio Rios, Javier Orozco and Rodolfo Pizarro selected.
Debutants Luis Venegas and Erick Torres were also included.
After a relatively subdued start to the game, with neither side able to create anything clear-cut, Mexico made the breakthrough courtesy of Layun in the 18th minute.
The 26-year-old full-back pounced on a rebound to fire the ball into the roof of the net after Torres' initial shot was saved by Bolivia goalkeeper Vaca.
Bolivia struggled to possess the ball for large parts of the opening 45 minutes as Mexico pegged the South Americans back in their own half.
It was an onslaught from Mexico in the closing stages of the first half, with Bolivia fortunate to be trailing by just the solitary goal at the break.
Mexico thought they had a penalty three minutes into the second half after Aquino was bundled over in the area but American referee Chris Penso awarded a goal kick.
As Mexico keeper Munoz remained untroubled, Herrera's men continued to pose a threat at the other end and came within a whisker of doubling their lead just past the hour mark after Layun almost caught Vaca off his line.
Vaca was forced into action against just minutes later, denying Torres from close range.
Bolivia did have a chance in the first minute of injury time to salvage a draw but Ronald Eguino's header cannoned back off the post.
