The defending champions survived a difficult opening half hour and had goalkeeper Gianluigi Buffon to thank as they came from behind to win 4-1 at Cagliari.
Florenzi's opening 25th-minute goal for Roma, who lost their unbeaten league record at Juventus a week ago, was the day's highlight and not even the player seemed to believe it as he ran to the touchline with his hands on his head.
Genoa appeared to have survived the danger when a Francesco Totti free kick hit the wall but a defender lofted the ball into the area and Florenzi, with his back to goal, met it with a majestic overhead shot which went in off the foot of the post.
Roma stalwart Totti added the second with a deflected shot on the half hour, Maicon finished off a counter-attack two minutes before the break for the third and defender Mehdi Benatia completed the scoring early in the second half, the Moroccan's fifth goal of the season.
Genoa's misery was completed with a bizarre sending-off for midfielder Matuzalem, who was given a second yellow card for gesturing to Roma fans as he was being substituted.
His replacement Isaac Cofie, who had already run onto the pitch, had to be taken off, although the Ghanaian was brought on again four minutes later for Andrea Bertolacci.