Bologna pressed for much of the second half but fell 2-0 down with 10 minutes left when Rodrigo Palacio took his time to plant home a measured finish from range.
Inter looked home and dry but were dragged into extra time when Alessandro Diamanti and Manolo Gabbiadini both scored in a frantic finale. A tight additional 30 minutes saw the match drifting to penalties before Andrea Ranocchia's header proved the difference on 119 minutes.
Here, Sports Mole dissects two hours of entertaining action between two sides desperate to keep their chances of silverware alive.
Was the result fair
Bologna have every right to feel hard done by after battling back bravely during normal time. They showed attacking intent from the outset but met an Inter keeper in fine form. While Samir Handanovic kept the visitors out, Inter were clinical when it mattered to make the final four.
Inter Milan's performance
5/10 Andrea Stramaccioni's side looked sluggish in the first half and despite a strong response after the break they soon dropped deep and played on the counter. Palacio, Javier Zanetti and Guarin drove the hosts forward throughout and their quality made the difference at crucial times.
7/10 Diamanti and Alberto Gilardino used their skill and experience to cause Inter problems right from the first whistle. The tactically astute visitors swamped the midfield and controlled possession, but their fine work in the final third was ultimately undone by some sloppy defending in the closing stages.
Sports Mole's man of the match
Alessandro Diamanti The mercurial playmaker dropped off into intelligent areas and gave the Inter backline a torrid time from set pieces. His superb free kick was reward for a display full of passion and quality. The Italian international did not deserve to be on the losing side this evening.
Luca Banti had a quiet game, with just a handful of cynical tackles that required his intervention as both teams tired.
Inter: The Nerazzurri must recover quickly as a daunting trip to the Olimpico awaits this weekend as Inter face Roma in a clash of Champions League contenders.
Bologna: It's back to the scene of the crime for Bologna as they make an instant return to the San Siro this weekend, with AC Milan their opponents on Sunday afternoon.