Serie A wrap: Juve stay perfect
Genoa's young attacker Ciro Immobile gave his side a shock lead at home when he turned at the top of the penalty area in the 18th minute and slotted the ball past Juventus goalkeeper Gianluigi Buffon.
Juventus came into Sunday's match with two wins from as many games and showed the resilience of a champion side to pull off their third-successive victory.
Emanuele Giaccherini started the reigning champions' comeback in the 61st minute with a grand strike from outside the box after being teed up by substitute Mirko Vucinic.
Vucinic put Juventus in front from the spot 17 minutes later after fellow substitute Kwadwo Asamoah won the penalty.
The Ghanaian midfielder wrapped up the victory when he tapped in Vucinic's cross in the 84th minute.
Juventus remain top of Serie A with nine points, ahead of Lazio and Napoli on goal difference.
Lazio defeated Chievo Verona 3-1, while Napoli won by the same margin over Parma to match Juventus' 100 perfect start to the season.
In Italy's capital, Zdenek Zeman's inconsistent return as Roma's head coach continued after his side gave up a two-goal lead to lose 3-2 to Bologna.
Roma struck after just six minutes when Alessandro Florenzi headed home the rebound after Francesco Totti's strike cannoned off the post and the home side made it 2-0 in the 16th minute when Erik Lamela cut inside and placed his left-foot shot inside the far post.
But three second-half goals from Bologna ensured Roma remain winless at home this season.
A strong header from Alberto Gilardino got the visitors going in the 72nd minute and just 60 seconds later Bologna were level when Alessandro Diamanti got clear to slot the ball home.
Gilardino completed the visitors' shock comeback in the 90th minute when he took advantage of a defensive mix-up to tap the ball into the net.
In the late kick-off, Inter picked up their second win of the season with a 2-0 triumph at Torino.
Deigo Milito opened the scoring in the 13th minute, but the visitors had to wait until the final five minutes to make sure of the points when Antonio Cassano slotted home.
In other Serie A results, Sampdoria knocked off Pescara 3-2 in a clash of two newly promoted sides, Siena drew 2-2 with Udinese and Fiorentina defeated Catania 2-0.