Esteban Cambiasso's equaliser for the hosts five minutes from time cancelled out Ciro Immobile's superb individual goal as second-placed Inter nudged up to 35 points, nine behind Juve after the champions won 3-1 against Cagliari on Friday.
Genoa remain second bottom on 14 points.
Inter's Rodrigo Palacio twice went close early in the second half, first blazing over after finding himself one-on-one with Genoa keeper Sebastien Frey and then forcing a fine save from the Frenchman with a powerful left-foot strike.
A stout Genoa defence easily kept Inter at bay and Immobile hit them with what looked like a fatal sucker punch with 13 minutes left.
His fine individual goal saw him ghost past defender Andrea Ranocchia and slip a smart finish under keeper Samir Handanovic.
Cambiasso brought Andrea Stramaccioni's side back into the game with a thumping header but despite late pressure, Inter could not grab the winner and now look increasingly unlikely to take the title from their rivals.
Napoli will be looking to get their season back on track after having two points deducted in midweek when they visit Siena at 1400 GMT while fellow Champions League hopefuls Lazio and Fiorentina are also both away, at Sampdoria and Palermo respectively.
The weekend's big game takes place at the Stadio Olimpico in Rome (1945 GMT) where flamboyant AS Roma take on a resurgent AC Milan led by red-hot striker Stephan El Shaarawy. (Writing by Terry Daley; Editing by Mark Meadows; email@example.com; +44 20 7542 7933; Reuters Messaging:; firstname.lastname@example.org)