The home side controlled the game from the get go, with Alessandro Florenzi's wonder-goal the highlight of a convincing victory.
Goals from Alessandro Florenzi, Francesco Totti, Maicon and Mehdi Benatia saw off the challenge of the midtable visitors, who had Matuzalem sent off in the second half to compound their woes.
The Giallorossi were in control from the first whistle, but it still took a moment of brilliance for them to break the deadlock after 25 minutes. A Totti free kick was not cleared, and Florenzi was quickest to the bouncing rebound, placing a superb overhead kick into the far side.
Totti made it 2-0 on the half-hour mark, profiting from a smooth Gervinho cutback to slot a placed shot into the bottom corner from the top of the box.
Maicon got in on the act moments later, sprinting into the box to convert Florenzi’s superb ball and finish off a splendid Roma counterattack.
Roma added yet another early in the second half, as Benatia rose highest to guide home a Totti corner past a static defense.
Genoa was never in contention, and its misery was complete on the hour mark when Matuzalem, on his way out of the game via a substitution, was sent off for mouthing off to the taunting Roma fans.
The win keeps Roma two points ahead of third-place Napoli, and within eight points of Serie A leader Juventus.