The result keeps Antonio Conte's Blues top of the table with seven points from three matches, while Roma trail the Premier League champions by two.
Edin Dzeko and Eden Hazard each bagged a brace for their sides, but it was David Luiz who opened the scoring after just 11 minutes with an impressive strike.
The Brazil international defender saw his attempted through ball knocked back into his path before curling in an unstoppable shot from 25-yards out.
Roma worked their best chance of the opening half-hour in the 31st minute -- Radja Nainggolan forcing a fine reflex save from Thibaut Courtois after a well worked move from the visitors.
Though Chelsea capitalised six minutes later, upping their advantage to two goals through Hazard, who volleyed home Alvaro Morata's chipped lob after a swift counter-attack.
Their advantage wouldn't last long, however, as Roma worked a deserved opener thanks to a stunning individual effort from former Manchester City left-back Aleksandar Kolarov, who nutmegged a defender and fired high and past a stranded Courtois after the ball took a slight deflection.
Roma pulled level in the 64th minute through Dzeko, who sensationally volleyed Federico Fazio's long ball with his left foot from inside the box.
Dzeko surprisingly gave Roma the lead six minutes later -- the former City striker guiding home Kolarov's cross from a set piece toward the far post.
But Chelsea were unbowed, and Hazard collected his second of the day with a quarter-hour to play, slotting a header of his own across goalkeeper Alisson and into the far netting from a Pedro cross.