Potosi had not won since February 2 but leapt from fourth into second in the Liga del Futbol Profesional Boliviano with victory over the reigning Clausura champions.
Dino Huallpa struck first for Potosi in the 18th minute and the visitors led 2-0 at half-time thanks to Darwin Pena's strike with four minutes until the break.
Just seven minutes after half-time and it was 3-0 with Ivan Zerda scoring for Potosi and although Juan Carlos Arce struck in the 69th minute for the home side, Bolivar never got close to reeling the visitors in.
Bolivar, who followed up their Clausura title in 2012/13 with a second-placed finish behind The Strongest in the 2013/14 Apertura season, slumped to a fifth game without victory in all competitions.
The La Paz-based club sit 10th in the 12-team competition with seven points from six matches.
The Strongest also continued their poor start to the Clausura season, going down to LFPB leaders Universitario 2-1.
Mauricio Saucedo scored either side of half-time for Universitario, while Jair Reinoso gave The Strongest some hope with a goal just four minutes after the home side's second.
The Strongest sit sixth with 10 points from seven games, while Universitario top the LFPB standings with 14 from the same number of fixtures.
In the game of the round, Oriente Petrolero triumphed 3-2 on the road at Blooming with Ronald Raldes scoring a 91st-minute winner.
In other matches, San Jose thrashed Nacional Potosi 4-1, Guabira drew 1-1 with Wilstermann and Aurora cruised to a 3-0 victory over Sport Boys.
