The visitor, without the suspended Luis Suarez and Edinson Cavani, had too much for the host, which finished the game with 10 men following Jair Torrico's sending off.
Uruguay kicked off its World Cup 2018 qualifying campaign with a 2-0 victory over Bolivia thanks to goals from Martin Caceres and Diego Godin in La Paz.
The defensive duo struck in either half for Oscar Tabarez's side in the opening game of the qualifying campaign in South America, earning the visitor its first win in Bolivia since 2007.
An open encounter saw both goalkeepers called into action on a number of occasions before Caceres broke the deadlock with a calm finish.