Neither team cound find a breakthrough in the first half, but the introduction of Fredy Guarin during the halftime interval changed the course of the match, as the Colombian set up Antonio Cassano for the opener in the 50th minute, before adding the second with a deflected 20-yard effort.
Inter had numerous chances to further extend their lead but was forced to play out the last 10 minutes nervously after goalkeeper Luca Castellazzi was injured with all three substitutes already used, forcing Rodrigo Palacio to mind the net.
The incident came too late for Verona, as it could not take advantage of the misfortune of the Nerazzurri, who now await their opponents in the quarterfinals.
Both sides started the match positively, though it was Inter who fashioned the first chance 13 minutes in. Palacio found himself in a good shooting position on the edge of the box, but elected to square to McDonald Mariga, who could not find the target.
Verona quickly went on the attack, and Juan Jesus was forced to make a timely intervention to snuff out a dangerous cross by Paulo Grossi, who then dinked just wide after collecting the loose ball. The Siena loanee was proving to be a real handful for the Inter defense, and he was at the center of things once again as he released Daniele Cacia for a shot on the turn that brushed off the outside of the post.
Cassano then went close with a free kick that was bent the wrong side of the post, before Armin Bacinovic responded in kind for Verona with a set piece that flew just off target.
The best opening of the first half fell Inter’s way just before the interval, as a sublime one-two between Palacio and Ricky Alvarez saw the latter denied from point-blank range by the alert Rafael in the visitors’ goal.
Andrea Stramaccioni threw on Guarin for Mariga to start the second half, and within 10 minutes of his introduction, the midfielder turned the match on its head.
The Colombian won the ball in the Verona half and wasted little time to slip in Cassano, who sprinted clear of the last defender, rounded Rafael, and slotted home to open the scoring.
Guarin was not finished, as four minutes later, he doubled Inter’s advantage when he converted from the edge of the box via a deflection after a neat link-up with Cassano on a set piece.Verona should have made it 2-1 with 20 minutes left. Alessandro Carrozza’s delivery found Valeri Bojinov inside the area. His first touch took Matias Silvestre out of the equation, but with the goal at his mercy from six yards out, the substitute whacked the ball into orbit.
Bojinov would then play the role of provider, flicking for Cacia, whose half volley forced an acrobatic save from Castellazzi, who was forced to hand the gloves to Palacio after injuring himself in the landing.
The Argentine proved to be a more than able deputy between the posts, making an impressive save on Carrozza in stoppage time to preserve the clean sheet for Inter and seal the club's progression.