Marco Ferrufino's men were expected to dismiss the challenge of bottom club Potosi, and took the lead three minutes before half-time when Marcelo Gomes tucked away his left-footed shot from a cross.
The Estadio Jesus Bermudez hosts had been under pressure at the back from multiple Potosi chances in the first half, but had been on the verge of preserving their league lead when disaster struck.
Pastor Torrez's long-range strike bounced in front of San Jose's goalkeeper and into the back of the net for a stunning equaliser on 85 minutes.
And there would be more pain to come for the home side, as Enrique Diaz scored an own goal to hand the strugglers their fifth win in 18 matches - helping them off bottom spot.
Diaz had looked to pass back to his goalkeeper but his effort went wide of the mark - and after a desperate lunge from the shot-stopper failed to halt the ball in its path, it trickled towards the goal before bouncing in off the right post in calamitous fashion for the hosts.
San Jose remain top of the table on goal difference from Club Universitario, who failed to capitalise on the leaders' slip up as they drew 2-2 on the road at The Strongest.
The Strongest started the weekend in third spot but were looming to go level on points with San Jose as they took a two-goal lead inside 14 minutes.
Alejandro Chumacero and Pablo Escobar were both on target early, before Universitario ensured they remained in second spot with a stirring fightback.
Ruben Cuesta pulled a goal back on 30 minutes, before Martin Palavicini equalised with 12 minutes to play.
Real Potosi consolidated fourth spot in the league with a 2-0 win at home to fifth-placed Bolivar.
Maximiliano Andrada's third-minute strike gave Real the advantage, before the three points were sealed when Dino Huallpa doubled their lead late on.
Real sit five points behind leaders San Jose, and just three points off a continental competition spot.
Aurora's winning streak ended at three matches, as they were held to a 1-1 draw away at Sport Boys.
Marcos Ovejero scored first for Sport Boys, before Aurora snatched a point courtesy of Oscar Diaz's 80th-minute effort.
Oriente Petrolero snapped a four-match winless run in thrilling fashion, holding on for a 4-3 win over Blooming - with the latter falling to the foot of the table due to Nacional Potosi's success.
Petrolero trailed 2-0 on the brink of half-time, before pulling a goal back just prior to the break via Alejandro Melean.
Gualberto Mojica then struck a brace, and Alcides Pena added a fourth, but they had to hold on after Pablo Salinas pulled a goal back late for Blooming.
Wilstermann were 2-0 victors over Guabira, helping them climb over their opponents into ninth spot after two wins from three matches.
