Thibaut Courtois was Real Madrid's hero in the shootout
Karim Benzema's penalty put the European and La Liga champions ahead but Samuel Lino levelled just after half-time to make it 1-1 in Riyadh.
Madrid won the shootout 4-3, scoring all their kicks, while Eray Comert missed his and Thibaut Courtois saved Jose Gaya's effort.
Real Betis face Barcelona in the second semi-final on Thursday.
"Obviously as a goalkeeper you have to study penalties," Courtois said.
"Gaya missed his last one against Sevilla on the left, and scored his last one down the middle against Betis, so we knew he was going to shoot there."
--- Courtesy of BBC Sport