The midfielder's early volley ensured Diego Simeone's side, without injured talisman Diego Costa, denied Barca a seventh successive appearance in the last four.
Atletico once again proved masterful at negating the threat of Lionel Messi, who failed to score for the fifth successive match against the club on an electric night at the Vicente Calderon.
With the scoreline finely poised at 1-1 after the first leg at Camp Nou, both sides knew there was everything to play for. But it was Simeone's men who held their nerve.
Atletico was dealt a huge blow when leading marksman Costa, who limped out of the first leg with a hamstring injury, failed to recover in time, but his replacement took just five minutes to help raise the roof.
Adrian Lopez powered a strike against the crossbar and, after David Villa had done well to keep the move going and delivered a cross to the back post, Lopez leapt impressively and nodded the ball into the path of Koke, who slotted home from close range.
Atletico continued to take the game to its Liga rivals and on 10 minutes Villa smashed a shot against the upright after latching on to Koke's disguised through ball.
A few minutes later Messi, unmarked seven yards out, missed a great chance when he headed Dani Alves' cross just wide.
When Alves next darted forward, he was robbed of possession on the edge of the Atletico box by Lopez, who held off the challenge of three opponents as he carried the ball into the Barcelona half before drawing a foul from Sergio Busquets, who was booked.
From the resulting free kick, Atletico worked the ball forward to Villa, who held off Marc Barta and unleashed a shot from an acute angle against the crossbar.
Neymar then produced some exquisite trickery to work his way past two opponents before squaring the ball for Messi, who failed to control his close-range shot.
Barcelona had the better of the possession throughout the remainder of the first half, but it failed to create anything of note, although Lopez and Cesc Fabregas both had faint penalty appeals turned down.
Three minutes after the restart, Barcelona almost restored parity. Xavi slid a defense-piercing throughball to Neymar, who attempted to take it around goalkeeper Thibaut Courtois. The Belgium international dived down to push the ball away from the Brazil forward and Messi elected against shooting from the rebound and was crowded out.
Just before the hour, Alves' cross found Xavi unmarked, but the diminutive midfielder could not keep his glancing header on target.
Lopez went off to a standing ovation on the hour, and his replacement Diego, whose wonder goal earned Atletico a draw in the first leg, swiftly forced Jose Pinto into a smart save.
After 70 minutes, Gabi raced clean through, albeit from an angle, but his tame shot allowed Pinto to save with his feet, before Raul Garcia's goal-bound strike from inside the area was blocked.
After 77 minutes, Neymar's header went agonizingly wide for Barcelona and that was the last chance they had to prevent a famous defeat.
Substitute Cristian Rodriguez almost put the game well beyond their reach in the last minute, but Pinto dived to his right to push the ball out for a corner.
It mattered not, as Atletico played the clock down near the Barcelona corner flag to join Chelsea, Real Madrid and Bayern Munich in Friday's semifinal draw.