The tie was delicately poised entering the match following a 1-1 draw in the first leg last week, but Sevilla recorded a two-goal success in front of their own supporters to triumph 3-1 on aggregate.
Sevilla boss Vincenzo Montella made six changes to the team that started against Eibar in the league at the weekend.
Jesus Navas and Gabriel Mercado came into the back four, while Ever Banega replaced Roque Mesa in midfield. There were also three changes in the final third as Franco Vazquez, Joaquin Correa and Luis Muriel all featured.
As for Leganes, head coach Asier Garitano made sweeping changes from the team that started against Getafe. Indeed, only Diego Rico and Javier Eraso kept their spots, with the likes of Nordin Amrabat, Nabil El Zhar and Claudio Beauvue all returning to the team.
It was the visitors that had the first half-chance of the match in the third minute, but Beauvue could only turn a low Amrabat cross wide of the near post.
Sevilla were dangerous in the wide positions though, and Correa almost picked out Pablo Sarabia with a cross in the sixth minute, only for Rico to make a vital clearance as the play flowed from end t end.
The home side took the lead in the 15th minute, however, when Correa turned home from close range after Muriel had managed to scoop the ball towards his teammate.
Leganes were sinking deeper and deeper as Sevilla dominated the ball, but the visitors had a couple of positive moments on the counter-attack, with Gabriel firing into the arms of Sergio Rico 15 minutes before the break.
Beauvue then headed over the home side's crossbar, before Banega and Sergio Escudero both had efforts cleared off the line down the other end in the latter stages of the first period.
Beauvue curled a free kick over the Sevilla crossbar in the early stages of the second half as Leganes looked to answer back, before Ruben Perez just missed Rico's post with a strike from distance.
Sarabia tested Leganes goalkeeper Nereo Champagne with a powerful strike in the 67th minute. The score, however, was still 1-0 to Sevilla with 20 minutes to play at the Estadio Ramon.
Both managers made changes in the period that followed, but clear chances remained few and far between as Sevilla closed on a spot in the final of the competition.
It might have been a nervy final few moments for the hosts, but Vazquez found the top corner with a super effort in the 89th minute to ensure that Montella's side would triumph courtesy of a 2-0 home success.
Sevilla will take on either Valencia or Barcelona, who meet on Thursday night for the second leg of their semi-final, in the final of this season's competition.
SEVILLA (4-2-3-1): Rico; Navas, Mercado, Lenglet, Escudero; N'Zonzi, Banega (Pizarro 84'); Sarabia (Layun 74'), Vazquez, Correa; Muriel (Sandro 80')
LEGANES (4-2-3-1): Champagne; Tito (Mantovanni 84'), Bustinza, Siovas, Rico; Gabriel, Perez; Eraso (Brasanac 58'), Amrabat (Garcia 73'), El Zhar; Beauvue