A stunning Alessandro Florenzi overhead kick was followed by goals from Francesco Totti, Maicon and Medhi Benatia as the Giallorossi bounced back from their first defeat of the season last weekend.
Genoa ended the game with 10 men after Francesco Matuzalem was shown a red card on the hour mark.
Genoa made a confident start but it proved to be a false dawn and they fell behind when Totti earned a free-kick just outside the area in the 25th minute.
The Roma captain lined up a free-kick which was blocked by the wall, the ball eventually looping up to Florenzi who, with his back to the goal, chose the acrobatic approach with an overhead kick which could not have been more accurate, hitting the right-hand upright on its way in.
Roma laid siege to the Genoa goal and they break through for a second time when Totti's shot deflected inside the helpless Mattia Perin's near post.
It was the 37-year-old's first goal since October 5 and his first at the Olimpico since March.
Maicon added a third to crown an emphatic first-half performance with Totti getting the ball rolling on a punishing counter-attack from deep in his own half.
Dodo sent Florenzi out wide and his cross served Maicon with just Perin to beat, and the Brazilian full-back made no mistake, beating the Genoa goalkeeper from close range.
There was no let-up in the second half either with Totti's corner headed in by Benatia for his fifth goal this season.
Things went from bad to worse for Genoa when they lost Matuzalem to a second yellow card, even though the referee took a while to produce a red, only doing so after consulting with his assistant.
By that time, Matuzalem had left the field, substituted by Isaac Cofie, who was then ordered to leave the field, and leave Genoa with 10 men.
They could have had nine, in Totti's opinion, when his shot was blocked on the line by Thomas Manfredini, although the Genoa defender appeared to use his upper body and not his arm.
Mattia Destro came on to provide even more firepower to the Roma attack and, in truth, he should have added his name to the scoresheet, but he lifted his best chance over the bar with only Perin to beat.
Enough damage had been done, though, with Roma winning comfortably and remaining eight points adrift of Juve, but importantly two ahead of Napoli, who won at Hellas Verona.