De Rossi was also involved at the other end in the first period, clearing a Goran Pandev shot off the line after Roma goalkeeper Morgan De Sanctis could only parry the initial shot towards his own net.
Playing against his former club for the first time since leaving them this summer, De Sanctis was fortunate again in the final stages of the half when he was saved by the woodwork.
Pjanic showed far more precision and composure with his free kick in first-half stoppage time, a powerful effort which curled away from Pepe Reina and into the top corner.
Substitute Cannavaro, booked shortly after being brought onto the field as a replacement for Miguel Britos moments prior to Pjanic's goal, was cautioned again in the process of giving away a second-half penalty.
He was given his marching orders after pulling down Marco Borreillo, and Pjanic stepped up from 12 yards to net Roma a second goal which secured them their eighth consecutive league victory this term.
The capital outfit now have a five-point lead over second-place Napoli, for whom this was the first defeat of the campaign, at the top of the table.