Serie A leader AC Milan exited the Coppa Italia following a 1-0 last-16 loss to Lazio at Stadio Olimpico on Thursday.
Maurizio Sarri's hosts avenged Saturday's 1-0 league defeat by Milan thanks to an 80th-minute header from captain Mattia Zaccagni.
Christian Pulisic, who missed the weekend's game with a muscular problem, made his return off the substitutes' bench after Milan went a goal down but the United States attacker saw a late effort saved as last season's finalists crashed out.
Bologna, who beat Milan in the final in May, also reached the quarterfinals on Thursday with a 2-1 win over Parma. Bologna and Lazio will now face off in the last eight.
Lazio scored the only goal of the match from a corner that probably shouldn't have been awarded.
Milan defender Pervis Estupiñán headed away a free kick and the ball appeared to hit Lazio's Alessio Romagnoli on the way out, but the referee awarded a corner to the home team.
Zaccagni was left unmarked to head that into the back of the net.
Bologna's match appeared to be heading for penalties before substitute Santiago Castro headed in a cross from Emil Holm in the 89th minute.
Serie A struggler Parma had taken a surprise lead in the 13th minute when Adrian Benedyczak ran onto a through ball from Mathias Løvik and slotted past Federico Ravaglia.
But Bologna, which won the competition for the first time in 52 years last season, leveled shortly before halftime.
Jonathan Rowe's initial attempt hit the post but the English winger controlled the rebound and fired it home for his first goal since joining Bologna in August.
There was another positive note for Bologna as Ciro Immobile came on as a late substitute for his first appearance since a thigh injury in August.
Information from The Associated Press and PA was used in this report.