Rudi Garcia's side went straight for the jugular, snatching an early lead through the in-form Alessandro Florenzi, who picked up the rebound after Bologna goalkeeper Gianluca Curci could only parry Miralem Pjanic's free kick.
The Giallorossi doubled their advantage in the 16th minute when former Arsenal man Gervinho beat Curci with a low strike following a swift counter-attack.
Roma were three to the good with 25 minutes on the clock as Mehdi Benatia volleyed home a corner to claim his second goal in as many matches.
Gervinho added a fourth in the 64th minute with a fine individual goal, the Ivorian leaving his marker for dead and curling a clinical finish into the top corner.
Adem Ljajic completed the rout in the 86th minute with a cheeky lob after being put through on goal by Pjanic.