Juve suffered their first league defeat since March as Gianluigi Buffon's 500th Serie A appearance was soured by Luca Antonini's 94th-minute winner.
Buffon looked set for a 238th top-flight clean sheet on a frustrating night for the three-time defending champions, who saw Fernando Llorente and Angelo Ogbonna denied by the woodwork.
Genoa goalkeeper Mattia Perin then made two good saves to deny Juve substitute Alvaro Morata as the final whistle approached.
While Juve shaded proceedings, they were by no means dominant, with the effects of a fourth game in 12 days there for all to see.
And they were hit with a late blow as Genoa substitute Alessandro Matri - formerly of Juve - drew the attention of two defenders before cutting the ball back to the unmarked Antonini, who unconvincingly prodded home from six yards.
The loss was only Juventus' second in Serie A in 2014 and saw Roma move level on 22 points courtesy of their 2-0 success against struggling Cesena.
Mattia Destro opened the scoring after eight minutes, converting Gervinho's assist.
And Daniele De Rossi wrapped up the three points with an effort nine minutes from time.
Mauro Icardi's 90th-minute penalty earned Inter a 1-0 win over Sampdoria as they eased the pressure on coach Walter Mazzarri.
Under-fire Mazzarri found himself up against one of the reported favourites to replace him should he be sacked, in the shape of Sampdoria coach Sinisa Mihajlovic, but he came out on top against the ex-Inter defender.
The hosts were wasteful in the first half, with Rodrigo Palacio in particular spurning several good chances, but they managed to snatch a dramatic late triumph, with Icardi - who spent two seasons with Sampdoria - slotting home his spot-kick after Alessio Romagnoli had brought down Zdravko Kuzmanovic.
Third-placed Milan dropped points for the second game in succession, but were grateful to Giacomo Bonaventura for rescuing a 1-1 draw at Cagliari.
Victor Ibarbo's deserved first-half opener was cancelled out by Bonaventura's sublime 30-yard lob.
The hosts steadied themselves in the second period and looked the more likely to win the game as Daniele Conti struck the post with a free-kick, but they had to settle for a point.
Napoli missed a chance to go third after a 1-1 draw at lowly Atalanta.
Ex-Napoli man German Denis fired Atalanta in front in the 57th minute but Gonzalo Higuain's 86th-minute effort meant the spoils were shared, despite Atalanta seeing Luca Cigarini sent off for a second bookable offence late on.
Elsewhere, Khouma Babacar's double led Fiorentina to a 3-0 home win over the fifth-placed Udinese, while Palermo and Torino claimed 1-0 wins over Chievo and Parma respectively.
