The two sides went into Sunday's match tied on 21 points and five points shy of 17th-placed Genoa and it seemed that Palermo would leave their opponents behind when Anselmo opened the scoring just before half-time.
But the Sicilians' long wait for a first win since November - a run now stretching over 14 games - continues as goals from Innocent Emeghara and Alessandro Rosina left them staring at a return to the second tier after nine years at the top.
Siena suffered an early bout of nerves with Palermo full-back Andrea Dossena given free reign to test keeper Gianluca Pegolo with a firm drive outside of the area.
It was not long before Pegolo's opposite number found himself called into action, though, as Stefano Sorrentino reacted well to a bullet header from Rosina.
Pegolo looked lively again in the 25th minute as Mauro Boselli met Fabrizio Miccoli's corner, the Siena keeper pushing the ball over the crossbar, and soon Rosina was racing downfield unmarked to clip Matteo Rubin's pass just wide of the target.
But despite their opponents' dominance, it was Palermo who took the initiative in the relegation six-pointer as Anselmo found the back of the net one minute before the break.
Another Miccoli corner found the Brazilian perfectly placed to control the ball at his feet before turning it home to give Palermo a precious, and rare, half-time lead.
Anselmo was withdrawn for Nelson at the break and Palermo's good fortune went with him as Siena levelled in the 51st minute.
It was all too easy for Swiss striker Emeghara to tap home his fifth goal since joining the Bianconeri in January as Ezequiel Munoz clumsily blocked Sorrentino's path to collecting the ball.
Palermo pressed on and Boselli came close to rattling Pegolo with a decent header from Mauro Formica's right-wing cross in the 57th minute.
Siena would complete the turn-around 15 minutes later, though, as Rosina fooled Sorrentino from the penalty spot after Steve Von Bergen had brought Emeghara down in the box.
By now Palermo were desperate and Munoz lacked the required composure to head home Formica's corner with the final 10 minutes approaching.
And with time running out for Palermo, Nelson saw his powerful drive clatter the crossbar and spin away to safety as the seconds ticked away at the Barbera.