The home side started confidently, defying their league position and creating good opportunities in the opening quarter of the match, but Edgar Barreto and Jasmin Kurtic were among those who missed the target.
The away side finally created a good chance of their own in first-half injury time, but Marco Rossi shot wide from the middle of the penalty area.
After the break the stalemate continued as both sides struggled to keep any meaningful possession.
Midway through the second half Palermo brought on Mauro Boselli and the substitute almost made an instant impact. Only a great save by Frey denied the striker after he'd been put through by Ilicic.
With 15 minutes left, Salvatore Aronica was shown a second yellow card for a needless foul, and the home team were down to 10 men.
Genoa could not take advantage of the situation, though, and the game finished goalless.