Spanish playmaker Olmo was cleared to play again on a temporary basis before the game but the decision came too late for him or Pau Victor, in the same position, to feature against Copa del Rey winners Athletic.
Gavi put Barcelona ahead from close range after 17 minutes and teenage winger Yamal netted the second early after the break.
Spanish and European champions Real Madrid face cup runners-up Mallorca on Thursday in the second semi-final in Saudi Arabia, where the competition has been held for the past few years.
"Athletic are a very physical team that make you run a lot, we suffered above all towards the end, but we were able to play well and we're very happy," Yamal told Movistar.
The winger said Olmo and Victor were pleased to be allowed to play once more.
"In the end you're nervous when you can't play and when you get news like that, you're very happy," added Yamal.
Barca coach Hansi Flick hailed the decision from Spain's national sports council regarding Olmo and Victor.
"The whole club is very happy for this right decision," said Flick, hoping to win his first silverware at the helm of Barca.
"We wanted to show we are a team and we win also for them."
Barcelona, who qualified as La Liga runners-up, started brightly and Raphinha volleyed over from a fine Jules Kounde cross and forced Unai Simon into a good save with a free-kick.
It was no surprise when the Catalans broke the deadlock with Alejandro Balde cutting the ball back for Gavi, playing in Olmo's attacking midfield role, to turn home for his first goal since suffering a severe knee injury last season.
The 20-year-old pointed at an imaginary watch in his celebration, a nod to Olmo who regularly produces the same gesture after scoring.
At the other end Inaki Williams dallied on the ball too long as Athletic's best attacking move of the first half broke down.
Yamal, returning after an ankle problem, should have added Barcelona's second after Raphinha's shot was saved but the 17-year-old miscued an attempted lob.
Wojciech Szczesny, on his second start in goal for Barcelona, made a good save to keep Inaki Williams at bay before the break.
Sharp Yamal
Barcelona doubled their lead early in the second half when Gavi slipped in Yamal who finished with aplomb.
Veteran Polish forward Robert Lewandowski spurned a fine chance to add the third, firing off-target when well placed.
Athletic coach Ernesto Valverde, who was sacked as Barcelona boss after a defeat at the same stadium in 2020, brought on Nico Williams to try and turn the game around.
The Spain international, heavily linked with Barcelona in the summer, was not fit enough to start, but made a positive impact from the bench.
The winger set up Oscar de Marcos to strike but the Athletic defender had strayed just offside and the goal was ruled out.
Inaki Williams also had a goal ruled out for offside after Frenkie De Jong's poor back-pass took a slight deflection off Alvaro Djalo on its way to the Ghana international.
"It's a shame given all the effort... but we have good things ahead of us and we have to continue," said Inaki Williams.
Barcelona were able to book their place in Sunday's final, in which Olmo will be allowed to feature.
"We don't care (who we face in the final), it will be hard and we want to win it, which is the important thing, and go back home with the trophy," said Yamal.
