The home side dominated the game, but were floored by an goal from the Spaniard after an hour and Diego Simeone's side march on
The capital outfit, who lifted the trophy in 2010, have progressed by a 5-2 aggregate scoreline thanks to a superb smash-and-grab display at Mestalla.
Atletico were kept under severe pressure by Valencia for the best part of an hour, but a fantastic goal from Adrian calmed their nerves and set them on their way to victory.
The only blot on their performance was a late red card to Tiago, who will now miss the final after his involvement in a fracas following a penalty appeal.
Goals were definitely on the agenda for Valencia who, with a 4-2 deficit to overturn from the first-leg in the capital, set out their stall to attack right from the start.
The hosts had plenty of possession inside the opposition half during the opening exchanges, but the lack of a final ball prevented them from really testing Thibaut Courtois inside the Atletico goal.
That all changed after 20 minutes, when a snap shot from Sofiane Feghouli was parried by the Belgian keeper after a nick off Jonas, who was also thwarted from the rebound.
The Algerian had another go from distance moments later, but this time fizzed just over the bar.
Diego Simeone’s side were barely able to get a kick, and were forced to keep all 11 men behind the ball as the pressure and tenacity from Valencia was relentless.
Antonio Barragan twice was able to set up Roberto Soldado from the right flank, but both times the frontman failed to steer his effort on target.
Valencia just kept coming. Sergio Canales, starting his first match in Europe since September, drilled an effort low towards the near post from the left, but Courtois was again able to spread himself well and save.
But they were almost caught napping on the counter four minutes before the interval, as Arda Turan’s low cross was smothered by Diego Alves, inches away from the onrushing Falcao.
Valencia continued with the same cutthroat intensity coming out of the break, but as in the first-half, they were unable to get anyone on the end of their frequent forays into the opposition penalty area.
Atletico defended stoutly, and then, right on the hour mark, showed the hosts how it should be done.
Diego clipped a perfectly-weighted ball over the top of the defence towards Adrian, who took it onto his chest before ripping an unstoppable half-volley past Alves for his 10th goal in the tournament.
The pair combined again almost immediately after the restart, but this time, Alves was able to beat away Adrian’s powerful drive from the byline.
The Valencia keeper was called into action again to deny Falcao from close range as his side appeared completely floored by the Atletico goal that left them needing three of their own to qualify. To compound matters, Canales was carried from the field with what looked like a serious injury.
Tempers flared with 10 minutes to go, as confusion following an apparent handball in the area saw both sets of players square up to each other. Simeone even rushed off the bench to calm the ruckus, which ended when Tiago was shown his marching orders by the referee.
But their numerical deficit mattered little at this stage, and as a late Tino Costa effort was saved by Courtois, Valencia knew that their time was up.
Atletico will now square off against fellow Primera Division outfit Athletic Bilbao in the final, with a chance to regain the trophy they won in 2010.
Valencia meanwhile will need to regain their focus quickly, as they face a crucial trip to Malaga on the weekend in the battle for the third Champions League qualifying spot in the Primera Division.