The Bianconeri were creative in attack but were not able to make their chances count as they fall four points off AC Milan at the top of the table
Despite creating numerous opportunities, the Old Lady were unable to make the breakthrough, and AC Milan's win over Lecce means that Juve now trails by four points in the table.
It was an upbeat start to the first half, with Juventus goalkeeper Gianluigi Buffon forced to make a great save just 10 seconds in to deny Rodrigo Palacio's shot.
The visitors responded, however, and worked Sebastien Frey on two occasions in the following minutes. On the first, the Frenchman denied Simone Pepe's shot from inside the box, while he saved Claudio Marchisio's close-range shot shortly after.Genoa responded near the half-hour mark and gave Buffon a major scare, as Davide Biondini moved down the right flank and delivered a perfect cross into the six-yard box for Alberto Gilardino, who rose higher than his marker but powered his header over the bar.
Juventus will certainly curse its luck after coming out strongly in the second half, only to find the woodwork in the way of the opener every time.
In the 53rd minute, Mirko Vucinic flicked on a corner from the left and the ball smashed into the upright. Just five minutes later, the Montenegrin was unlucky again, as he connected well with a Pepe cross from the right, but his header hit the wrong side of the post.
On 60 minutes, it was Pepe's turn to hit the post as he was on the receiving end of an Andrea Pirlo free kick, and with only Frey to beat inside the box, the 28-year-old could not direct the ball goalwards.The Bianconeri were piling the pressure, but often at the expense of opening spaces at the back. In the 64th minute, Kakhaber Kaladze almost put Genoa up, but his shot from point-blank range went straight against Buffon after his initial header had been denied by the Italian goalkeeper.
Gilardino went close to scoring in the 78th minute, when he latched on to a through ball and rounded the onrushing Buffon, but from a tight angle, he screwed his effort high and wide.
In the dying moments of the match, Genoa had a penalty claimed waved away by the referee, as Marco Rossi fell to the ground after a sliding tackle from Pirlo. The replay showed that there was some contact, but the match official ignored the protests.
The draw leaves Juventus in further trouble, as it is now four points shy of leader AC Milan, while Lazio could get just within touching distance of the Bianconeri if it beats Bologna in Sunday's late match.