Josip Ilicic gave the hosts a flying start at the Stadio Renzo Barbera with a goal after just five minutes, but Manolo Gabbiadini brought Bologna level soon after.
Palermo searched for a winner, but could not find one as they were left inside the bottom three, two points adrift of Siena and safety.
Bologna, meanwhile, can almost start planning for another season in the top flight given their 10-point cushion over the relegation zone.
With Siena winning on Saturday, Palermo needed three points to get back level with the Tuscan side and they could hardly have made a better start to the game.
After only five minutes, they were ahead with Ilicic curling a shot past Gianluca Curci from Fabrizio Miccoli's lay-off.
Ilicic could have doubled Palermo's lead five minutes later when he again combined well with Miccoli, but this time could not get enough accuracy on his shot to beat Curci.
Everything seemed to be going well for the home team until a mistake by Stefano Sorrentino gifted Bologna an equaliser.
He gestured to pick up the ball from Massimo Donati's backpass, realising only at the last second that he could not handle it. His attempt to smother the ball with his body failed with Gabbiadini accepting the opportunity to bring Bologna level.
The Sicilians were stunned, but responded well with Miccoli hitting the post late in the first half as they continued to attack.
There was little change in the second half with the Rosaneri sending men forwards in search of a winner.
This saw them leave gaps at the back which were nearly exploited by Cristian Pasquato and Alberto Gilardino, who missed the best chance of the second half in the 75th minute when he failed to beat Sorrentino in a one-on-one situation.
Sorrentino denied Gilardino again moments later before Palermo saw their appeals for a penalty waved away at the other end when Jasmin Kurtic went down inside the area.
Tempers flared in stoppage time with three yellow cards shown, but amongst the confusion, Palermo were unable to find a precious winner.