The hosts entered the game on the back of successive victories which had pulled them out of the relegation zone while Genoa were attempting to end a run of five games without a win which has seen them steadily slide down the Serie A table.
But the visitors made the better start and they should have taken the lead in the 12th minute.
Giandomenico Mesto but a brilliant ball into the Cesena box but Genoa forwards Houssine Kharja and Mattia Destro both failed to get a touch with the goal at their mercy.
Marcio Rafinha fired in an effort from distance for Genoa in the 20th minute but Francesco Antonioli made an easy save.
There was another chance for Genoa after 34 minutes but former AC Milan defender Kaka Kaladze could not finish from Omar Milanetto's inviting cross.
Cesena's only meaningful effort on goal was a speculative effort from Luis Jimenez which flew high over the bar.
The siege continued in the second half as Destro, on loan from Inter Milan, fired wide from the edge of the box, but the visitors were given a scare when Igor Budan headed just wide from a Luca Ceccarelli cross at the other end.
Destro missed another fine chance after 68 minutes. Domenico Criscito picked the striker out in the box, but the 19-year-old snatched at the chance as he fired wide.
Eduardo tipped Maurizio Lauro's cross over his own bar after a brief foray forward from the hosts before Kharja fired narrowly over the bar as time began to ran out for Genoa to make their dominance pay.
Emanuele Giaccherini could have stolen the points for Cesena with 10 minutes to go but his left-footed shot was dragged wide of the right-hand post.