Unai Emery's men raced into an early three-goal lead and then added a fourth in the second half despite having had Coke sent off
Trailing 1-0 from the first leg, the home side wasted no time in overturning the deficit, stunning Porto with three goals in the opening 29 minutes.
Captain Ivan Rakitic stroked home an early penalty and Vitolo put Sevilla ahead in the tie with a composed left-footed finish.
Carlos Bacca, who delivered a fine individual display, then produced a smart turn and finish to increase Sevilla's advantage.
Although Porto threatened to fight back following Coke's dismissal early in the second half, with Beto making fine saves to deny Ricardo Quaresma and Hector Herrera, Sevilla held firm and grabbed a late fourth through Kevin Gameiro prior to an injury-time consolation from Quaresma.
The omens are good for Unai Emery's side, as they won Europe's secondary club competition on the last two occasions they made it past the quarter-final stage - in 2006 and 2007.
Porto's return to the city where they won the competition in 2003 was not a happy one and they have now lost their last four games in Spain.
Both sides made enforced changes due to suspensions, with Sevilla missing Alberto Moreno and both Fernando and top-scorer Jackson Martinez absent for Porto.
Emery spoke in the build-up to the game about a need for patience, but his team clearly had other ideas as they blew Porto away with a blistering first-half display.
Fabiano was forced into a super save with his foot to deny Bacca after three minutes, but the respite was brief as Sevilla were awarded a penalty when Danilo was adjudged to have brought down the forward.
Rakitic stepped up to coolly send Fabiano the wrong way and give the hosts a fifth-minute lead.
Fabiano was in action again to repel a crisp half-volley from Jose Antonio Reyes, while Quaresma registered Porto's first effort of note after 22 minutes with a ferocious shot that Beto palmed behind.
Two goals in the space of four minutes then left the visitors with a mountain to climb. Fabiano's ill-judged throw out was seized upon by Fernando Navarro and flicked on by Bacca to Vitolo, who controlled beautifully before slotting into the bottom-right corner.
Bacca got in on the act in the 29th minute when he was allowed to turn and lash home his 20th of the season, with the aid of a deflection, from 15 yards.
Porto coach Luis Castro was sent to the stands shortly after half-time for speaking out of turn to the referee but he almost had cause for celebration in the 52nd minute when Beto tipped Quaresma's cross-cum-shot onto the crossbar.
The Portuguese side were given more hope two minutes later when Coke hacked down Quaresma and received a second yellow card and Beto then made a terrific save to claw away Herrera's deflected effort.
Quaresma flashed a low volley wide with Beto stranded soon after and the same player's cross 15 minutes from time glanced off the bar.
However, Sevilla weathered the storm and rounded off a superb night when Vitolo's centre was parried by Fabiano and Gameiro reacted quickest to slot home from close range.
Quaresma did manage a late consolation with a stunning injury-time strike that flew into the top corner, but it wasn't enough to stop the Sevilla party.
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