Roma climbed to fifth with 14 points after the win.
Roma's gung-ho attacking approach, a characteristic of seasoned Czech-born coach Zdenek Zeman, has turned them into a side where anything can happen.
Their attacking record of 18 goals scored in Serie A is bettered only by leaders Juventus, and their tally of 13 against is worse than everyone except lowly Pescara and Chievo, who have shipped 15 each.
This season has already seen them give a masterclass in winning 3-1 at Inter Milan, produce an abject display in a 4-1 loss at Juventus and throw away a two-goal lead in a 3-2 home defeat by Bologna.
Sunday's game began disastrously for them as Juraj Kucka and Bosko Jankovic swept Genoa to a 2-0 lead in only 15 minutes.
Thirty-six-year-old Francesco Totti, in his 21st season at his only professional club, pulled one back from inside the penalty area in the 28th minute and Pablo Osvaldo hooked in the equaliser one minute before the break.
That set up a second half of Roma dominance which saw Osvaldo head them in front in the 55th minute and Argentine midfielder Erik Lamela curl his shot into the bottom corner with seven minutes to play.
At San Siro, Inter started with five Argentine players in their line-up while their Sardinian opponents had eight.
Two of Inter's Argentines set up the opening goal when Diego Milito pulled the ball back for Esteban Cambiassio, he crossed to the back post where Cassano scored with a header in the 28th minute.
- Sports & Recreation
- Zdenek Zeman