The well-supported Sicilians, more used to fighting for European places in recent seasons, remain six points adrift of fourth bottom Genoa but in the end will be pleased with the stalemate despite again being booed off.
Palermo defender Salvatore Aronica was sent off for a naive second booking midway through the second period while Genoa had the best chance in the first half through Marco Borriello.
The game was the only one in Serie A on Saturday with the big focus on Sunday when faltering Inter Milan host resurgent AC Milan and their former Inter striker Mario Balotelli.
Leaders Juventus welcome coach Antonio Conte's former side Siena in Sunday's main programme of matches.
