Unai Emery's side began the night trailing 1-0 in the tie, but were in control after just 30 minutes as they scored three times.
Captain Ivan Rakitic's fifth-minute penalty was followed by quick-fire goals from Vitolo and Carlos Bacca.
Porto remained in the contest thanks to the 54th-minute dismissal of defender Coke, which rules him out of the first leg of the semi-final, but substitute Kevin Gameiro killed off the visitors 11 minutes from the end.
Ricardo Quaresma scored the goal of the night in stoppage-time, but it was no more than consolation for Porto.
Sevilla will find out their last-four rivals in Friday's draw in Nyon.
Emery's side have now won 10 of their past 13 matches which has not only seen them push for European honours, but leave them on the cusp of the Champions League places in the Primera Division.
By contrast Porto's only hopes of silverware now lie in the Portuguese Cup, where they face league leaders Benfica in the semi-finals later this month.
Interim boss Luis Castro had called on his side to score early and pile the pressure on Sevilla.
Instead, they watched on as the hosts ran away with the tie.
It took five minutes for Bacca to win the penalty that Rakitic converted to cancel out Eliaquim Mangala's goal in last week's first leg in Portugal. Bacca was tripped by Danilo and skipper Rakitic then sent Fabiano the wrong way.
Sevilla kept pressing and Vitolo almost got a touch to Coke's cross before Fabiano kept out Jose Antonio Reyes' volley.
It was no surprise when Sevilla went ahead in the tie on 26 minutes.
Vitolo ran by a couple of defenders to get on to Bacca's header before side-footing past the exposed Fabiano.
Three minutes later Bacca made it 3-0 with a 12-yard strike and Porto appeared to be heading out with a whimper.
Coke's dismissal on 54 minutes meant the Portuguese champions were able to build up a head of steam in the final half-hour, but without finding the goal to set up a nervy finale.
They had their chances though, with former Porto goalkeeper Beto clawing Hector Herrera's deflected effort away off the post.
Quaresma passed up two more good chances before substitute Juan Quintero lashed over.
Sevilla then sealed their progress when substitute Gameiro latched on to a loose ball to score on 79 minutes.
Quaresma smashed a 20-yarder into the top-left corner to provide Porto with some cheer as they went out of the competition.