French winger Giuly stopped a certain goal with his hands and Swedish striker Zlatan Ibrahimovic made no mistake from the spot to open the scoring in the first-half.
Simone Perrotta leveled the score but Roma's joy didn't last for long. Hernan Crespo and Julio Cruz scored one goal apiece and Ivan Cordoba ensured the victory in the second-period.
The Nerazzurri became in charge of the league table with 14 points, three clear of second-placed Roma.
In the 29th minute, Cesar capitalized on Perrotta's slip to go through on goal but his initial shot was blocked by Roma keeper Alexander Doni.
The ball rebounded to Ibrahimovic, who lobbed towards the net but Giuly used his arm to clear the ball.
The former Barcelona midfielder was sent-off before Ibrahimovic successfully converted the resulting penalty.
Roma drew level eight minutes after the interval when David Pizarro pounced on Maxwell's sluggishness to steal the ball before squaring to Perrotta; whose low shot went into the net.
Substitute Crespo restored Inter's lead four minutes later when he volleyed home on the rebound after Esteban Cambiasso's shot was denied by Doni.
Crespo's compatriot Cruz, who also came off the bench, added the third on the hour mark through a left-footed shot.
Colombian defender Cordoba completed the rout in the 67th minute as he connected with Luis Figo's cross at the far post to head into the back of the net.