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Nicolo Cambiaghi was the match-winner for Bologna, scoring in the 111th minute to silence the Roma faithful and set up a quarter-final clash against Unai Emery's Aston Villa.

After Zeki Celik's last-ditch intervention denied Santiago Castro early on, Jonathan Rowe found the back of the net with a stunning finish into the top-right corner in the 22nd minute after being picked out on the edge of the box.

That lead lasted only 10 minutes as Evan Ndicka headed in from Lorenzo Pellegrini's corner, although Bologna was back ahead before the break as Federico Bernardeschi scored from the penalty spot after Stephan El Shaarawy brought down Nadir Zortea in the box.

The visitors made it 3-1 in the second leg early in the second half as Castro smashed the ball past Mile Svilar after great persistence from Rowe, but Roma received a lifeline when Remo Freuler fouled Robinio Vaz and Donyell Malen scored a spot-kick of his own in the 69th minute. 

Pellegrini, who twice went close from free-kicks either side of half-time, restored parity in the tie with a finish from distance that was out of Federico Ravaglia's reach with 10 minutes of normal time remaining. 

There was little to separate the two sides in extra-time, but with nine minutes to go, Thijs Dallinga played an inch-perfect pass for Cambiaghi, whose shot hit the inside of the near post before nestling in the far corner.

It looked as if Roma was destined to win after recovering from a 3-1 deficit in the second leg, but Bologna refused to give up at Stadio Olimpico.

It looked as if Vincenzo Italiano had taken Rowe and Castro off too soon, with the two forwards leading the Bologna fight. Rowe created a match-high four chances, while Castro recorded the most shots for Bologna (three), but it worked out in the end.

Italiano, who was a two-time UEFA Conference League runner-up with Fiorentina, was thrilled as his side regroup to set up a last-eight clash with Aston Villa.

"You saw the atmosphere in the stadium from the start, we were against a strong side and I said our odds were 49-51 to go through," he said.

"But we managed to turn them around and continue in an important European competition.

"The match was wonderful. We are truly happy to come here and do what we did, which was to climb the mountain.

"I can only congratulate the lads for an extraordinary performance, as winning in this atmosphere against this Roma side was a genuine achievement.

"We got through a tough league phase, won a difficult play-off and have now beaten a team that is superior to us in every way. However, playing your cards in the best way brings you to these results.

"We go in again [against Villa] knowing that we are the underdogs, but we'll prepare something and try to do something else extraordinary."

Meanwhile, Roma is now without a win in five matches in all competitions, with the home fans making their frustration heard at the final whistle.

Midfielder Bryan Cristante rued the Giallorossi's UEFA Europa League exit, but urged his team-mates to respond in a positive manner.

"We shouldn't have conceded all these goals," he said. "We went behind, we did so well to get back into it, seemed in control during extra-time and ready to score the decisive goal. But, instead, it went the other way.

"We are all disappointed to be out of the competition. The fans let us hear their disappointment. It's tough, because we had got it back on track. We were convinced we had the right approach, but we lost.

"We were there, we were in the right position to get through to the next stage of the Europa League. We cannot complain about fatigue, we've just got to roll our sleeves up and keep going,"