The Catalan giants hit the headlines at the start of the week when former president Josep Maria Bartomeu was among those arrested on Monday - he was then provisionally released under charges of unfair administration and corruption of business - as part of a police investigation into last year's 'Barcagate' scandal.
Barca's players looked anything but affected by off-field events, however, as they dominated the majority of the second leg, Ousmane Dembele giving them a richly deserved first-half lead.
Lucas Ocampos had a penalty saved by Barca goalkeeper Marc-Andre ter Stegen with 17 minutes to go and Gerard Pique made him pay by making it 2-2 on aggregate right at the end of stoppage time, moments after Sevilla had seen Fernando sent off.
Martin Braithwaite put Barca in front early in extra time and Luuk de Jong - who had been substituted - was shown a red card for dissent after Sevilla were not awarded a penalty, with the hosts going through to face Athletic Club or Levante in the final.
Dembele opened the scoring in the 12th minute in a scintillating Barca start, showing excellent close control in the penalty area before drifting outside the box to find the top-right corner with a sublime right-footed finish from 20 yards out.
The Blaugrana were causing Sevilla all sorts of problems with their slick passing and movement in a relentless first-half display, Marcos Acuna clearing a deflected shot from the brilliant Lionel Messi off the line.
Barca were almost level when Jordi Alba's acrobatic volley rattled the crossbar and there was more drama when Ocampos' tame penalty was saved by Ter Stegen after the Sevilla player had been upended by Oscar Mingueza.
Substitute Antoine Griezmann then produced the impact hoped for with time almost up, delivering an inviting cross for Pique to head home, this after Fernando was shown a second yellow card for upending Messi.
Barca were in front for the first time in the tie four minutes into extra time, Braithwaite coming off the bench to nod in Alba's superb cross.
Sevilla thought they had a second penalty for handball against Clement Lenglet but the VAR verdict ruled there was no intent, resulting in De Jong seeing red on a miserable night for the visitors.