The home side started the match well and were rewarded after just five minutes when a foul from Danilo in the box gifted them a penalty. Ivan Rakitic made no mistake from the spot, his strike levelling things on aggregate.
The home side then doubled their lead midway through the first half when Victor Vitolo lashed an effort into the bottom corner from close range.
On the half-hour mark, Sevilla sent the home crowd into raptures when Carlos Bacca extended his side's lead further, firing a low shot in from just outside the box.
Despite leading 3-1 on aggregate, the home side made life potentially difficult for themselves when they saw Coke sent off after a second yellow card.
However, Sevilla wrapped up the match with 10 minutes to go when Kevin Gameiro reacted quickest to a rebound to slot the ball past Danilo and make it 4-0 on the night.
Porto did, however, manage a consolation when Ricardo Quaresma sent a curling shot into the top corner in injury time, but at the final whistle it was Sevilla who were celebrating.