The reigning Super Cup champions were below their best again amid a difficult start to 2023, but Courtois excelled, making crucial saves and then decisively denying Jose Gaya in the shootout.
Madrid will go on to play either Barcelona or Real Betis, who play Thursday, in Sunday's final.
La Liga champions Madrid, facing the Spanish Cup runners-up, had chances to win the game within 90 minutes but needed Courtois to make a stunning reflex save from Fran Perez in extra time.
The Spanish Super Cup was first held in Saudi Arabia in 2020 in the current "final four" format – and will remain in the country until at least 2029, despite criticism over the hosts' human rights record.
Madrid coach Carlo Ancelotti, who was without recently injured duo Aurelien Tchouameni and David Alaba, started with Nacho at left-back and brought Fede Valverde into the midfield trio.
Los Blancos started strongly, with Benzema producing a glorious dribble, but Cenk Ozkacar did well to cut him off and block the French striker's shot.
Courtois kept out Edinson Cavani's header and then did enough to put off Toni Lato, who burst in from the right and appealed in vain for a penalty when he slipped.
Madrid took the lead shortly before halftime when Eder Militao played a fine ball over the top to send Benzema through.
The forward was clumsily felled in the area by Eray Comert and tucked away the resulting penalty, sending Valencia goalkeeper Giorgi Mamardashvili the wrong way.