Frenkie de Jong's brilliant header had given Ronald Koeman's side the advantage before Mikel Oiarzabal's cool spot kick levelled things up at 1-1, where the scoring ended and the game went to spot kicks.
But cool heads were missing on penalties as five of the 10 efforts were missed, allowing Riqui Puig to roll home the crucial kick to send Barca into the final.
So who were the best and worst players on the pitch?
✔️ GOOD PERFORMANCE
Mikel Oiarzabal: 7.8
The brilliant little playmaker is fast becoming one of the finest talents in Spanish football and here, he looked like a Barcelona player of the future.
Always looking, always probing, he completed two dribbles and well as making a Big Chance for a team-mate, but his off-the-ball work was equally impressive.
He won 2/3 tackles, 7/12 duels and made a game-high 12 recoveries as he produced an equally disciplined defensive display, either side of rolling home a gorgeous penalty to level the scores in normal time. He'll be disappointed his almost perfect record from the spot was ruined by his miss in the shoot-out.
❌ BAD PERFORMANCE
Ousmane Dembele: 6.5
Ousmane Dembele continues to blow hot and cold and sooner or later the excuses attached to his injuries will need to be forgotten and he needs to deliver.
He has been better in recent weeks but regressed back to his former self, losing the ball an astonishing 40 times. Losing the ball a lot isn't too big of a deal for a creative player - but only if he is creating, and Dembele isn't.
Too often he made the wrong decision in the final third, and while he completed a very high six dribbles - which shows exactly what he is capable of - his overall contribution needs to be more.
⭐ STAR MAN
Antoine Griezmann: 7.8
The former Atletico Madrid wide man was excellent in scoring twice at the weekend in the defeat of Granada, and he took his form into this match, particularly with Lionel Messi missing.
The Frenchman's brilliant cross found the head of Frenkie de Jong for his side's only goal of the contest, and as well as that he completed three dribbles and created another Big Chance that was squandered.
Griezmann also only lost possession six times despite being creative and actively involved - a real step in the right direction for him. Let's just never mention his miss in the shoot-out...