After soaking up an hour of pressure from the hosts, Atletico ended the tie as the former Deportivo striker expertly controlled the ball on his chest before rifling an unstoppable half-volley into the top left corner.
The match was soured by a needless sending off for Tiago, who lost his temper and slapped Roberto Soldado after mistakenly believing the referee had awarded a penalty to Valencia in the closing stages: no such decision had been made, and the Portugal midfielder now misses the final.
There was also a nasty-looking knee injury to Valencia's on-loan playmaker Sergio Canales. Having suffered a similar injury at the start of the season, he may well have played his last game for Los Che.
With the hosts needing to overturn a 4-2 first-leg deficit, the onus was very much on them to attack.
And attack they did, creating a hatful of first-half chances but failing to take them as a combination of stout defending and good goalkeeping denied Los Che.
Atletico, meanwhile, elected to sit back, the strategy apparently simply to avoid capitulation - although Valencia had other ideas.
Rojiblancos right-back Juanfran almost gave away a penalty, aided by the honesty of Canales who had miscontrolled the ball in the box, while Sofiane Feghouli’s spectacular volley from a corner was well-saved by Thibaut Courtois via a deflection off Jonas.
That was Valencia’s best opportunity as, while they dominated possession for the rest of their half, stout defending from the likes of Joao Miranda limited them to half-chances as Soldado met two low crosses on the slide but could only put wide and over respectively.
Courtois made another decent save, from the frustrated Soldado this time, as Valencia kept piling it on but Diego Simeone’s men reminded them of their qualities with two chances on the counter attack, both snuffed out by quick thinking from goalkeeper Diego Alves.
The second half started surprisingly cagily, Valencia perhaps stung by those two late Atletico opportunities, with the closest they came a smart piece of interplay between Canales and Jordi Alba that was snuffed out by the excellent Miranda.
Just before the hour mark there was a blow for Los Che as talented young playmaker Canales, on loan from Real Madrid, twisted his knee after an awkward landing, the former Racing Santander starlet in agony as he was stretchered off: he suffered a serious knee injury at the start of the season, and another long spell on the sidelines beckons, meaning his time at Valencia is probably up.
Within seconds their European campaign was over too, as from nothing Adrian scored a memorable goal, his 11th in the competition: the summer signing took a long ball on his chest, allowed it to bounce and struck a ferocious half-volley past the diving Alves and into the top corner.
They nearly had a second immediately afterwards as Diego’s mazy dribble allowed the strangely-quiet Radamel Falcao to shoot straight at Alves, but the sting was taken out of Valencia and the match as a whole.
Late on there was a ridiculous incident that saw Tiago given his marching orders, the Portuguese losing his head after a bizarre ‘penalty’ incident: after a high ball into the Atletico box, the referee was alerted by the assistant to a handball in the area.
Pointing for a free-kick to Atletico - Tino Costa had handled - both sets of players mistakenly believed he was signalling a penalty, as Tiago’s arms were also raised. In fact he had done nothing of the sort, but a mass fracas developed that saw both sides engage in the kind of handbags normally reserved for a Friday night in suburban England.
During the shenanigans, Tiago slapped Soldado, while Alba hurled himself to the deck feigning assault: Tiago was dismissed, led away by his team-mates as Simeone tried to calm his charges, while Alba was booked for his embarrassing tumble.
It was a sour end to the clash, although a man to the good Valencia tried to claw back the deficit in the closing stages: the closest they came was a low shot by Jeremy Mathieu, cleared off the line by Diego Godin, deep into injury time.
Fortunately the whistle was greeted with more gentlemanly conduct, hands shaken all round as Atletico celebrated a second final in three years.
Valencia, meanwhile, must turn their attentions to holding on to the third automatic Champions League qualifying slot - and the future of coach Unai Emery, tipped to leave the Mestalla this summer.