The Estadio Jesus Bermudez hosts got off to the ideal start, as Juan Zampiery's run down the right side of the pitch resulted in his strike going in off the left upright after just one minute.
Adan Bravo doubled San Jose's lead in Oruro with a stunning effort, curling a right-footed shot into the top corner from outside the area on 14 minutes.
The Strongest pulled one back six minutes prior to half-time, as Luis Melgar tucked away into an empty net after San Jose's goalkeeper made a save off the crossbar.
However, Carlos Neumann reinstated San Jose's two-goal buffer before the interval, heading home at the back post much to the home fans' joy.
Neumann doubled his match tally and made it 4-1, when he tucked away a low shot after some brilliant team play in the build-up.
Roly Sejas dealt The Strongest more pain, as he finished a dazzling run from outside the area with a neat finish.
Alejandro Chumacero gave the visitors something to cheer about on 66 minutes, smashing home a left-footed strike, however, San Jose would not halt their rampage.
Bravo chipped his second of the game past the onrushing The Strongest goalkeeper, before Neumann wrapped up his hat-trick with a long-range header that dribbled through to round off the scoring.
Leaders Club Universitario have a three-point gap at the top, after their narrow 1-0 win at home to Real Potosi.
Universitario have 41 points through 21 games and are well-placed to win the title, ahead of San Jose (38), The Strongest (37) and Real Potosi (36).
Oriente Petrolero are fifth, five points shy of Real Potosi, after a 1-0 home win over Aurora, who fell to sixth.
Bolivar lost their third match in succession, going down 2-1 at Guabira, while Wilstermann are unbeaten in four - including three victories - after a 4-2 success over bottom club Blooming.
Sport Boys sit in ninth, but are just one point behind the seventh-placed Bolivar, after a 3-2 road win over Nacional Potosi.
