The Nerazzurri halted their rotten run of results by picking up a point on their travels, but the afternoon belonged to the hosts who will play top-flight football again next term
The Grifone, who secured their survival thanks to Palermo's 1-0 defeat at Fiorentina, were unlucky to have been rewarded for their first-half performance, although Tommaso Rocchi could have swung the match in the visitors' favour were it not for the crossbar.
The Ligurians came flying out of traps as within the first 10 minutes, Marco Borriello evaded his marker to send in a towering header, but Samir Handanovic pulled off a miraculous finger-tip save to deny the forward.
Their relentless start to the match showed no signs of abating as Antonio Floro Flores then unleashed a strike from the edge of the box that stung the palms of the Slovenian who read the situation aptly.
Genoa were clearly in the knowledge that only a win would do to ease their relegation fears for another season, and so it showed. Inter, on the other hand, initially seemed content to adopt a counterattacking style.
Marco Rigoni was the next to fashion an opening, but his strike - which appeared to be heading goal-bound - cannoned off a Rossoblu team-mate and the chance soon went begging.
And with just seconds of the first half remaining, Andrea Bertolacci's beautiful curling attempt from the D was again stopped in its tracks by Handanovic's equally-impressive reflexes.
The second period failed to inspire much of an improvement, and the opening stages of the period saw both teams happy to settle into a lull, although Inter were afforded more of the ball.
And their increased emphasis on a short passing game was almost rewarded as on the hour mark, Rocchi found space on the edge of the box and pinged the ball onto the corner of the stanchion.
The tempo continued to nose-dive, with both teams' fate having already been decided, and a point was the most fitting outcome in the Italian port town.