It was the home side that started the better and they might have taken the lead with an effort from Bosko Jankovic after five minutes, but he fired wide from close range.
However, it was Palmero that took the lead after 14 minutes when Luigi Giorgi headed past Sebastien Frey from close range. It might have been 1-1 when Marco Borriello struck a low effort just before the 30-minute mark, but it moved wide of the target.
Both sides had chances in the latter stages of the half, but it was Genoa who levelled five minutes into the second period when Borriello finished from close range. Palermo had a chance to move ahead after 65 minutes, but Michel Morganella struck wide from inside the box.
The home side appeared the most likely to secure the three points in the latter stages, but it remained level with both sides sharing the spoils.