Inter fumbled a 2-0 lead, including a spectacular Jeison Murillo overhead kick, as Bologna forced extra time, but Antonio Candreva secured the Coppa Italia victory.
The winners go on to face Lazio or Genoa in the Quarter-Finals.
Gabriel Barbosa was given his first start, seen his playing time limited to brief cameos as a substitute in Serie A. The visitors named a strong side, with Mattia Destro, Godfred Donsah and Blerim Dzemaili all included.
Inter fumbled a 2-0 lead, including a spectacular Jeison Murillo overhead kick, as Bologna forced extra time, but Antonio Candreva secured the Coppa Italia victory.
The winners go on to face Lazio or Genoa in the Quarter-Finals.
Gabriel Barbosa was given his first start, seen his playing time limited to brief cameos as a substitute in Serie A. The visitors named a strong side, with Mattia Destro, Godfred Donsah and Blerim Dzemaili all included.
It was the Nerazzurri who had the first chance of the game on nine minutes, but Eder fired a free-kick over the crossbar. At the other end, Destro say his shot blocked after a quick Rossoblu break had allowed him space in the Inter box.
Gabigol had his first chance of the game on 23 minutes, cutting in from the right before unleashing a left-footed shot. His effort appeared to be going wide, but Angelo Da Costa saved it nonetheless.
It had been a scrappy first half, but there was nothing scrappy about the goal which put Stefano Pioli’s side in front. Roberto Gagliardini’s corner looked a lost cause, but centre-back Jeison Murillo improvised with a stunning overhead kick to put Inter ahead.
It was 2-0 shortly afterward. Joao Mario picked the ball up on the right, and sent a fantastic pass in for Rodrigo Palacio, who made no mistake with his low finish.
That looked to have put the hosts firmly in control of the match, but Blerim Dzemaili’s strike from outside the box deflected off Geoffrey Kondogbia and into the net to give the Rossoblu hope.
The Nerazzurri looked to put the game to bed early in the second half, with Palacio seeing an effort blocked on the line and Eder firing just wide from the edge of the box.
Palacio had another chance to put the game to bed on 66 minutes, but the Argentina international saw his right-footed shot beaten away by Da Costa.
Joao Mario was next to try his luck, but his powerful strike from the edge of the area was too close to the Bologna ‘keeper.
Inter would be made to pay for their profligacy, with just under 20 minutes to play. Anthony Mounier sent in a deep cross from the left, and Donsah, unmarked at the back post, rose to head the ball past Juan Pablo Carrizo.
Just a minute before the equaliser, Inter had thrown on Mauro Icardi and Antonio Candreva for Gabigol and Palacio, and the captain just failed to make contact when given the chance to put the Beneamata back in front.
The Round of 16 tie went to extra time and Bologna seemed the brighter, as Federico Di Francesco’s pass for Oji Okonkwo was cleared practically off the line by Gary Medel.
Instead, Inter restored their lead when Icardi sprung the offside trap and rolled cross, Candreva’s finish taking a deflection off Marios Oikonomou to wrong-foot Da Costa.
Icardi rolled another splendid assist for Joao Mario, but the Portugal international was exhausted on the counter and couldn’t keep it on target.
Inter 3-2 Bologna (aet)
Murillo 33 (I), Palacio 39 (I), Dzemaili 43 (B), Donsah 73 (B), Candreva 98 (I)
Inter: Carrizo; D’Ambrosio, Medel, Murillo, Ansaldi; Gagliardini, Kondogbia; Gabigol (Candreva, 71), Joao Mario, Eder (Brozovic 93); Palacio (Icardi, 72)
Bologna: Da Costa; Krafth, Oikonomou, Maietta, Masina; Donsah, Pulgar, Dzemaili (Nagy, 72); Di Francesco, Destro (Okwonkwo, 79), Rizzo (Mounier, 61)
Ref: Mariani