The hosts posed the greatest goalscoring threat, but were ultimately content with a draw which, with Palermo beaten by Fiorentina, ensured their place in the top flight next season.
For Inter, the draw ended a three-game losing streak, but it was only their fourth point in the last seven matches, meaning they have little to play for when they host Udinese next weekend, on the final day of the season.
Genoa started brightly with Samir Handanovic making a fine save to keep Inter on terms in the 10th minute.
He was at full stretch on the dive to push Marco Borriello's header wide.
The lively Borriello had another chance on the half-hour mark, but his shot was blocked by Esteban Cambiasso.
Towards the end of the half, Handanovic again made an excellent stop to keep Andrea Stramaccioni's men level, this time denying Andrea Bertolacci's effort, which was heading for the corner.
Borriello made a nuisance of himself again in the second half before Inter went close to opening the scoring.
Inter striker Tommaso Rocchi's shot from the edge of the penalty area struck the crossbar with goalkeeper Sebastien Frey beaten for the first time.
Borriello was given a standing ovation when he was replaced in the 87th minute with Ciro Immobile taking his place.
The applause was more born out of relief, however, with news that Palermo were being beaten and that the point was enough to keep Genoa in Serie A with celebrations greeting the final whistle.