Greif, who denied Brais Mendez's penalty during regular time, thwarted Mikel Oyarzabal's attempt at the beginning of the shootout, following a 1-1 deadlock after 120 minutes.
"In just four minutes, Real Sociedad took the lead as Brais Mendez skillfully curled a left-footed shot into the net after Ander Barrenetxea's powerful attempt rebounded off the post and back to him."
The first half was an even affair which saw Real Madrid lose Karim Benzema through injury after 15 minutes, but Benzema's replacement, Luka Jovic would be decisive in the second half.
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
Real Sociedad had lost their previous 24 league visits to the Camp Nou, but may have thought their luck was about to change when Willian Jose opened the scoring as Portu crossed back into the Barca