Miguel Zahzu's men were 2-1 victors at Universitario Cobija on Sunday thanks to Wilder Zabala's 90th-minute winner.
The result was enough for San Jose to top the Apertura standings with 13 points from six rounds, three clear of previous leaders Bolivar, who crashed to a 5-0 loss at Sport Boys on the same day.
San Jose - 1-0 winners over Nacional Potosi on Wednesday - continued where they left off as Gil Parada opened the scoring in the 11th minute at Estadio de Cobija.
Gabriel Valverde netted an own goal five minutes into the second half, much to the delight of Cobija.
Though, the visitors were handed a boost, when Nicolas Vaca saw red in the 56th minute.
Ricardo Verduguez was also sent off for San Jose in the closing stages but it mattered little as Zabala struck late on.
It was a forgettable day for Bolivar as Sport Boys ran rampant for their first league win of the season.
Sport Boys led by two goals after just 10 minutes through Jose Castillo and Julio Perez at Estadio Samuel Vaca Jimenez.
There was no way back for Bolivar from that point, Sport Boys scoring three unanswered goals in the second half courtesy of Anderson Gonzaga's brace and Maximiliano Andrada.
Bolivar dropped to fourth spot as Real Potosi and The Strongest both won.
Real Potosi preserved their unbeaten start to the season, edging Wilstermann 1-0.
The Strongest recorded a comprehensive 4-0 win at home to Blooming.
In other results, Mauricio Saucedo scored twice as Club Universitario snapped a four-match losing streak with a 4-3 victory over rock-bottom Petrolero Yacuiba.
And Oriente Petrolero accounted for Nacional Potosi 2-0 - climbing to fifth in the process.
