Bologna have won just two league matches this season, but would still have been confident of overcoming second-tier opposition on home soil.
However, after the game had finished 1-1 after normal time, Zouhair Feddal popped up with a 120th-minute winner – his first goal for Siena - to send the Serie B team through.
Siena had led through Francesco Valiani but Davide Moscardelli hit back for Bologna to force extra-time.
Parma progressed from the fourth round with a routine 4-1 victory over Varese at the Stadio Ennio Tardini.
Jaime Valdes opened the scoring after just five minutes to deal a blow to Varese’s hopes of pulling off a shock victory.
Parma then took complete control with goals early in the second half from Gianni Munari and Raffaele Palladino.
Aleandro Rosi also found the target for the home side and Loris Damonte's 88th-minute goal was no more than a consolation.
Frosinone, the lowest-ranked side in the fourth round, were unable to pull off another shock as they were beaten 2-1 at Avellino.
The Lega Pro I outfit claimed the scalp of Serie A club Cagliari in the third round, but their run came to an end on Tuesday.
Midfielder Angelo D'Angelo put Serie B side Avellino in front after 22 minutes and forward Luigi Castaldo doubled their lead eight minutes from time. Daniel Ciofani pulled a goal back right at the death for the third-tier club.
Spezia made light work of reaching the fifth round in a 3-0 defeat of Serie B rivals Pescara on Tuesday afternoon.
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