A 3-3 draw at San Siro this evening has seen the Nerazzurri progress comfortably from a quarter-final in which they were always in complete control of.
Goals from Nicolo Barella, Lautaro Martinez and Joaquin Correa sealed progression, after Fredrik Aursnes had given the Portuguese visitors brief hope late in the first half.
Two late goals from Benfica saw them avoid defeat on the night, but it was not enough as the Portuguese league leaders crash out.
Simone Inzaghi's side now have a blockbuster semi-final tie against local rivals AC Milan to come, after they saw off Napoli last night.
Last week's 2-0 success at the Estadio da Luz gave Inter a substantial cushion, and one they would have felt comfortable in hanging onto, considering the club have never lost a Champions League tie when leading by at least two goals from the first leg.
Their form domestically would have cast some doubt though, as they came into the fixture having failed to win any of their previous five league games.
Inzaghi reverted back to the same side that won in Lisbon last week, after a weakened lineup were beaten at home by Monza here at the weekend.
The opening stages of the game passed by without anything of note occurring, until a piece of brilliance by Barella opened the scoring shortly before the quarter-hour mark.
A fine one-two with Martinez after Inter won possession back in Benfica's half saw Barella then chop inside and pick out the top left-hand corner expertly, completely out of reach of Odysseas Vlachodimos in goal.
Benfica rarely threatened in the opening 45 minutes, with Alex Grimaldo stinging the palms of Andre Onana with a free kick - their first shot on goal after half an hour.
Martinez was penalised for a shove on Gilberto after beating Vlachodimos with a header, just minutes before a headed effort brought the tie back to life again.
Completely against the run of play, Aursnes met an excellent cross from Rafa Silva to beat Onana, who was given no chance by the direction and power on the header in the Inter net.
Going in at half time with the deficit still as it was, Benfica flexed their muscles a little more early in the second half with persistent pressure on the Inter rearguard and were perhaps unfortunate to not be awarded a penalty after Martinez lunged in on Aursnes in the box.
However, after weathering the storm, Inter put the tie out of reach when the ever-willing Federico Dimarco burst into the area on the overlap and squared the ball perfectly to give Martinez a tap in inside the six-yard box.
A first goal in nine games for the Argentine put Inter 4-1 up on aggregate and took the wind out of the sails of the visiting side.
With Inzaghi looking to manage the game, he introduced Correa who made an instant impact off the bench, receiving a pass from Dimarco on the left-hand side of the box and unleashing an unstoppable curling effort off the inside of the far post.
Going four goals ahead in the tie saw Inter become very complacent though, firstly when Marcelo Brozovic's slack pass out from the back went straight to David Neres, but the Brazilian winger was denied by the upright.
However, Benfica would get a consolation soon after, when Grimaldo's in-swinging set piece was flicked on into the far corner by Antonio Silva.
Benfica have not lost four competitive fixtures in the club's history, and that is what they were looking to avoid heading into stoppage time, and fighting right until the end, they found an equaliser with the last kick of the match.
Petar Musa collected a low cross from Grimaldo and spun inside the area to fire beyond a motionless Onana as Benfica levelled at 3-3 on the night in an all-action second leg.
Despite the late chaos, Inter sealed their progression 5-3 on aggregate, setting up the first Champions League Milan derby semi-final in 20 years.
With all eyes now set to be firmly fixated on the two-legged Derby della Madonnina at the start of May, Inter must ensure they maintain a fight for the top four in Serie A, and they face Empoli next on Sunday afternoon.
Benfica now have just one focus, ensuring they seal the Primeira Liga title, after their lead was cut from 10 points to four in just over a week, and Roger Schmidt's side face Estoril at home at the weekend.