Seydou Doumbia’s second goal in Italy and a wonderful Alessandro Florenz?? solo strike in stoppage time secured the three points.
Italy midfielder Florenzi raced almost the length of the pitch after dispossessing Tina Costa before ramming a powerful shot past Genoa keeper Mattia Perin that sent the home support wild with delight at overtaking their hated local rivals.
Roma’s second-straight win moves them up to 64 points, one ahead of Lazio, who were outplayed for large periods at Atalanta and could only manage a 1-1 draw.
Marco Parolo saved a point for Stefano Pioli’s under-par side with a spectacular bicycle kick 13 minutes from time after they went behind to a Giuseppe Biava header just before the hour mark.
Lazio stay four points ahead of fourth-placed Napoli after Rafael Benitez’s side beat AC Milan 3-0 in a game that saw Milan defender Mattia De Sciglio receive the fastest red card of the Serie A season so far.
De Sciglio, who was making only his second start since January, was sent off after just 50 seconds for a clumsy foul on Marek Hamsik that gave the hosts a first minute penalty.
The right-back was saved, however, by his impressive goalkeeper Diego Lopez, who took advantage of Gonzalo Higuain having to wait nearly a minute to take the spot kick by leaping to his right and punching the Argentine’s powerful shot wide.
Milan’s 10 men resisted for 70 minutes after that scare and even hit the post through Giacomo Bonaventura five minutes before half-time.
But three goals in six minutes from Hamsik, Higuain and Manolo Gabbiadini won the game for Napoli and kept them in the Champions League hunt.
Antonio Di Natale overtook Roberto Baggio in the all-time scoring charts with his 206th Serie A goal, which was enough for Udinese to win 1-0 at Verona, who had both Jacopo Sala and Rafael Marquez sent off.
Two goals in four first half minutes from Josip Ilicic and another from Alberto Gilardino just after the hour mark helped Fiorentina earn a 3-1 win over lowly Cesena.
Vincenzo Montella’s side are on 52 points, two in front of Genoa and one ahead of sixth-placed Sampdoria.
Inter Milan, meanwhile, were jeered off the San Siro pitch after a goalless draw with Chievo that leaves them in eighth place.