Esteban Cambiasso headed a late equaliser after Ciro Immobile had put the visitors ahead, but Andrea Stramaccioni's men lose more ground to Juventus in the Scudetto race
Having frustrated the hosts for large parts of the match, the Rossoblu thought they had stolen all three points when Ciro Immobile struck in the final quarter of the game, but while Esteban Cambiasso's late header earned a point for the hosts, the draw left their Scudetto ambitions hanging in the balance.
It took Inter just five minutes to carve out a clear-cut chance at San Siro, with Diego Milito missing Antonio Cassano's cross by just inches, allowing Andreas Granqvist to clear.
Moments later, Cassano cut inside and picked out another superb pass to find the run of Rodrigo Palacio, but the attacker's control let him down and Sebastian Frey was able to block the ball away.
After a frenetic opening period, the match became bogged down in the foggy conditions. Inter's passing was disjointed, with Ricardo Alvarez in particular guilty of conceding possession too frequently, while Genoa seemed content to sit back and try to hit on the counterattack.
Indeed, it was from some sloppy play from the hosts that the visitors carved out their best opening of the first half. Some clever footwork from Andrea Bertolacci allowed Immobile time and space to shoot from 20 yards, forcing Samir Handanovic into a one-handed stop low to his left.
The crowd's frustration was increasing as Inter continued to stutter, with most of their angst directed at Alvarez, whose hapless half-hour was brought to a close when he was replaced by Alvaro Pereira.
The Nerazzurri resorted to hopeful long balls from Cambiasso and Fredy Guarin in a bid to get the isolated Milito involved, while the visitors grew in confidence and could perhaps have tested Handanovic further before the break had their final ball been more intelligent.
Palacio had a glorious chance to break the deadlock shortly after the restart, but he could only fire over the bar from close range when played in by Milito. Moments later, Milito found Palacio again, but Frey parried his half-volley away from the near post.
As with the first half, Inter began to grow frustrated after an opening five-minute fervour: their territorial dominance was clear, but they lacked a playmaker-in-chief to turn their possession into meaningful chances.
And with 13 minutes left on the clock, the visitors took a shock lead. Inter once again conceded possession high up the pitch, and the ball was cleared up-field to Immobile, who twisted and turned past Ranocchia before firing low at Handanovic, who was unable to stop the ball squeezing beneath his body.
Ranocchia had a chance to make amends moments later when he headed just over from a corner, before Immobile went clear once again at the other end only for the attentions of Handanovic to force him wide and out of play.
Inter continued to push for an equaliser and, with just five minutes remaining, they found a way through: Cassano's cross from the left looped into the area onto the head of Cambiasso, who did very well to power the header past Frey at the near post.
Stramaccioni's men pushed for a winner and thought they had it in the 90th minute, when Milito turned inside the box and squared to substitute Marko Livaja, but the youngster somehow contrived to hit the post from just a yard out with the goal gaping.
The result leaves Inter trailing Juventus by nine points heading into the winter break, with the Bianconeri now firmly in control of the title race.