Eibar, Deportivo, Osasuna and Valencia also advanced to the next stage of the tournament, after winning on Wednesday, reports Efe.
Wissam Ben Yedder and Luciano Vietto - each with three goals - and Pablo Sarabia, who scored a pair, led Sevilla over the humble Balearic island club in the second-leg of the tie.
Eibar, who won the first leg 1-2 away, put up another three goals against Sporting on Wednesday to seal the win.
Second-division Hercules managed to hold mighty Barcelona 1-1 in the first leg, but conceded seven goals in Wednesday's contest at the Camp Nou stadium in Barcelona against a second string line-up.
Though Arda Turan scored thrice, the highlight was Paco Alcacer's first goal in official competition since joining Barcelona.
Valencia, who are struggling in La Liga, beat visiting Leganes 2-1 to secure their spot in the last 16.
Deportivo La Coruna overcame their 1-0 loss to Real Betis in the first leg, besting the Seville club 3-1 on Wednesday to win the battle for a berth in the next stage.
In Pamplona, Osasuna beat Granada 2-0 to advance 2-1 on aggregate after a 0-1 loss in the first leg.