Barcelona twice equalised in regular time but couldn't recover after Valverde scored from close range on a breakaway eight minutes into extra time.
Defending Super Cup champion Athletic Club will face Spanish league champion Atletico Madrid in the other semifinal Thursday.
The Spanish Super Cup is being played in Saudi Arabia again after the coronavirus pandemic transferred last year's edition back to Spain. The competition was moved to Saudi Arabia — and expanded from two to four teams in a “Final Four” format — as part of a deal reportedly worth 30 million euros a year until 2029.
The changes drew criticism from human rights activists and complaints from fans who preferred the competition stayed in Spain. Among those complaining was Athletic midfielder Raul Garcia, who said this week it made “no sense” to play the games away from Spain.
It was Madrid's fifth straight win over Barcelona and its 100th in 248 competitive matches against the rival. Barcelona has 96 wins.
It was a mostly even match but Madrid looked the more dangerous team throughout thanks to their counterattacks led by Vinicius Junior and Benzema.
The duo gave Madrid the lead in the 25th minute after Benzema stole the ball from Barcelona midfielder Sergio Busquets near the midfield line and fed Vinicius, who made a run into the area and beat goalkeeper Marc-Andre ter Stegen with a shot into the top of the net.
Barcelona equalised with a fluke goal near the end of the half. Madrid defender Eder Militao tried to clear a ball from inside the area but his shot bounced off Barcelona striker Luuk de Jong and then off the post before going over the line.
Benzema hit the post in the 69th, then a couple of minutes later put Madrid ahead again from close range off the rebound of a deflection by Ter Stegen following a cross by Dani Carvajal. Ter Stegen had stopped another Benzema shot just moments earlier.
Ansu Fati, who replaced De Jong in the 66th, levelled the match again in the 83rd with a header off a well-placed cross by Jordi Alba.
Valverde scored the winner after a fast counterattack by Madrid, converting a cross by Rodrygo from the right flank with Barcelona's defence heavily outmanned.
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