Los Che were heading through as Sofiane Feghouli, an own-goal and Jeremy Mathieu set up a home win but a last-ditch attack turned the tie on its head
Sevilla scored in the fourth minute of stoppage-time to cancel Valencia's comeback and reach the Europa League final in the most dramatic fashion on Thursday with a 3-3 away goal victory on aggregate.
Unai Emery's men headed into the Mestalla tie with a 2-0 advantage, but a Sofiane Feghouli strike from close-range quickly put los Che in the driving seat.
Bernat's inch-perfect cross was met by Jonas' head not long afterwards in the first half and the attacker's effort ricocheted in off Rojiblancos goalkeeper Beto's back to level the aggregate scoreline. The visitors clung on until the 70th minute, when Jeremy Mathieu sent the home fans delirious by knocking the hosts into the lead.
However, Juan Antonio Pizzi's men were punished for taking their foot off the gas as Sevilla threw every man forward and Stephane Mbia, who scored in the 2-0 first-leg win, rose highest at the near post to finish past goalkeeper Diego Alves after Coke's long throw was flicked on by Federico Fazio.
Sevilla will have been well aware of Valencia's never-say-die attitude after los Che overturned a 3-0 deficit to emerge as 5-3 victors in their quarter-final tie with Basel.
The hosts were without the suspended Paco Alcacer - scorer of a hat-trick in his side's sensational win against Basel last month - but Valencia still started brightly, with Jonas prodding an effort at Beto in the first two minutes.
Carlos Bacca scored the second in last week's first leg and he had a great chance to open the scoring this time around, only to skew wide of the target in the eighth minute.
It was the home side who would take the early lead, though, as Feghouli exchanged passes with Eduardo Vargas before showing great composure to cut inside Fazio and drive home via a slight deflection.
The Algeria international continued to wreak havoc, forcing Beto into a save after battling his way through the visiting defence, and Valencia were level in the tie in the 26th minute.
Bernat whipped in a sublime cross from the left for Jonas to meet with his head, and his powerful effort was tipped onto the woodwork by Beto. The ball then rebounded onto the goalline before eventually crossing the line off the keeper's back to send the Mestalla crowd wild.
Jose Antonio Reyes should have restored Sevilla's aggregate advantage nine minutes before the break, but his sliding effort from close range was superbly saved by goalkeeper Alves after Bacca's backheel across the face of goal.
Chances dried up in the second half, with extra-time looking an increasingly likely prospect, but Mathieu had other ideas with 20 minutes remaining - the centre-back reacted quickest when the ball fell loose from a corner, with his smart finish firing Valencia in front.
Sevilla applied some late pressure, knowing that just a single goal would prove enough, but chances were at a minimum.
That was until Mbia's telling impact, though, as Sevilla reached the final of Europe's secondary club competition for the first time since 2007, when they lifted the trophy.