Alessandro Diamanti had the first attempt on goal after five minutes, but his shot went just wide.
The home side continued to pile the pressure on Bologna as Bergessio hit the post with a header.
From the resulting corner, Sergio Almiron then gave Catania the lead, heading home to make it 1-0.
© PA Photos
Manolo Gabbiadini broke free for Bologna just after the restart, but his finish was way off target.
The away side continued to push forward and Alberto Gilardino came close after 70 minutes, but his header went wide.