Saucedo opened the scoring in the sixth minute and Gualberto Mojica doubled the lead from a free-kick 20 minutes later.
Uruguay coach Oscar Tabarez made two substitutions in the first half by fielding Edinson Cavani and Nicolas Lodeiro for Maximiliano Pereira and Walter Gargano, but they failed to have the desired effect.
Saucedo made it 3-0 shortly after the interval and completed his hat-trick soon after.
Luis Suarez scored Uruguay's consolation 10 minutes from time.
Bolivia claimed only their second victory on the road to Brazil 2014, while fifth-placed Uruguay would be playing a knockout tie with a CONCACAF team if the tournament finished today.
Bolivia coach Xavier Azkargorta is hopeful of making it to the World Cup, adding: "There are 21 points left. We must play the games.
"We'll keep fighting to be as high as possible in the standings. We don't lose faith."
Tabarez was unable to hide disappointment, adding: "Our form is not good. We must keep focused. There are seven finals remaining. Bolivia won deservedly."
Ecuador remain second in the standings thanks to a 1-1 draw in Venezuela.
Juan Arango put the hosts ahead with a long-distance shot in the fifth minute but Segundo Castillo equalised midway through the half.
In Asuncion, Paraguay finally celebrated a victory after five defeats in a row, as they beat Peru 1-0 thanks to a 53rd-minute header from Pablo Aguilar.