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.
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 afterward 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 knocked 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 quarterfinal 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 that 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 defense, and Valencia was 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 goal line before eventually crossing the line off the keeper's back to send the Mestalla crowd into chaos.
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 center 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 M'Bia's telling impact, though, as Sevilla reached the final of Europe's secondary club competition.