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.
Jaime Valdes opened the scoring after just five minutes to deal a blow to Varese’s hopes of pulling off a shock victory.
Aleandro Rosi also found the target for the home side and Loris Damonte's 88th-minute goal was no more than a consolation.
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.
