Josip Ilicic, Borja Valero and Giuseppe Rossi were on target for the Viola, who went into Sunday's match on the back of Thursday's 2-1 triumph over Dnipro that allowed Vincenzo Montella's side to secure top spot in Europa League Group E.
The result leaves Stefano Pioli's side in 19th place in the league and without a win in all competitions since October.
The home side started well and Juan Guillermo Cuadrado had his long-range effort in the opening exchanges saved by Bologna goalkeeper Gianluca Curci.
But it did not take the Viola long to take the lead as Ilicic slotted home left-footed from the centre of the Bologna goal after 13 minutes hitting the bottom left corner.
Alberto Aquilani tried his luck from outside the box minutes later but Curci put in a great save to deny a second.
And Serbia international Nenad Tomovic could have got onto the scoresheet but his shot from inside the box just narrowly floated over the bar, that was moments before Rossi had his chance saved by Curci.
But the home side's pressure finally paid off as Valero managed to beat Curci with a close-range shot from the centre of the Bologna goal for his six goal of the season.
The Rossoblu attempted to pull a goal back before the break but Alessandro Diamanti's effort from just inside the penalty box sailed wide of the far post.
Valero came close to scoring his second five minutes into the second half with a shot from outside the box but his chance was inches away from the left post before Bologna applied some pressure.
First Diamanti sent his free-kick from outside the box just over the crossbar, before Rolando Bianchi's header was too high for the target.
Against the run of play the home side went further ahead after 64 minutes as Rossi collected Valero's cross in the box and fired left-footed in the roof in net to record his 14th goal of the season.
Diamanti came close with two great chances in the space of three minutes but he was first denied by goalkeeper Norberto Neto before firing his second over the bar.