Marc-Andre ter Stegen saved twice and Pedri converted the deciding spot-kick as Barca beat Betis 4-2 in Thursday's shoot-out in the Saudi capital Riyadh.
Madrid beat Valencia, also on penalties, in the other semi-final on Wednesday, with the deciding match to take place on Sunday at the King Fahd Stadium.
Nabil Fekir equalised for Betis near the end of regulation time after Robert Lewandowski had given Barcelona a first-half lead.
The score was 2-2 after extra time, with Ansu Fati giving Barcelona an early lead before Loren Moron equalised again for Betis.
Betis played the final couple of minutes of extra time with 10 men after Andres Guardado was sent off for a second bookable offence.
"The match was super difficult, Betis made it tough for us," Ter Stegen said.
"In the end it's about making it to finals, and we've made it. You also need some luck in the shootout, and this time it was on our side."
It will be the first time Spanish powerhouses Barcelona and Real Madrid will meet in the Super Cup final since the competition was revamped and taken to Saudi Arabia in 2020.
"It will be a beautiful match," Ter Stegen said.
"Everyone here wants to see a match like this and I'm thrilled to be able to play in it and to try to win it."
Madrid will be trying to equal Barcelona's record 13 Spanish Super Cup wins, while the Catalan club will aim to lift the trophy for the first time since 2018.
The Super Cup used to be contested between the Spanish league champions and the Copa del Rey winners, but now the runners-up in both competitions also participate in a final-four tournament that was taken to the Gulf state in a lucrative deal for the Spanish soccer federation.
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