The Catalans picked up their first silverware of the season and gained revenge for their Spanish Super Cup defeat by Athletic in January with a convincing victory, DPA reported.
Sociedad ended a three-decade title drought on Saturday when it beat fierce Basque rival Athletic Bilbao 1-0 in the delayed 2020 cup final held in Seville
Levante have never played a cup final, but went into the game with a slight advantage after a 1-1 draw in Bilbao three weeks ago. A 0-0 would have seen them through.
Pedri was a surprise starter for Barca just days after being diagnosed with a calf injury, while Tomas Vaclik returned in goal for Sevilla on Wednesday, Xinhua news reports.
Barcelona on Wednesday night trailed 2-0 in the 88th minute before an own goal and a header from Jordi Alba saw them take the game to extra time, reports Xinhua news agency.
Zinedine Zidane rested some first-team regulars, but a side containing Lucas Vazquez, Marcelo, Isco and Casemiro should still have been far too strong for their rivals.
