Stephane Mbia gave them the nod, the midfielder heading into the net four minutes into stoppage time which took the Spanish side beyond domestic rivals Valencia on aggregate.
Mbia ran to the corner and called out in celebration. There was not enough time for the home side to deliver a response.
The Mestalla stadium had risen in volume as Valencia built up a 3-0 lead to take them within moments of the final. Mbia's dramatic late goal has instead taken Sevilla into a showdown with Benfica on May 14, after the Portuguese club eliminated Juventus 2-1 on aggregate with a goalless draw in Turin.
Sevilla had been favourites to advance from their tie having won last week's first leg 2-0. Their advantage was threatened after just 14 minutes, though, as Sofiane Feghouli struck to put Valencia ahead on the night.
An own goal from goalkeeper Beto some 12 minutes later and a goal from Jeremy Mathieu just 21 minutes from the end put Valencia 3-0 up and 3-2 ahead overall. They will instead reflect on a goal from Mbia.
They were just over a minute away from going through to the final when Federico Fazio flicked on a long throw into the penalty area and Mbia rose to direct a header into the net and silence the Valencia fans packed into the Mestalla.
Some will have heard of the drama unfolding in Turin, too, as Benfica's hopes of winning the tournament survived eight added minutes and two red cards shown to their side. Both Enzo Perez and Lazar Markovic were dismissed for the Portuguese champions, while MIrko Vucinic was sent off for Juventus.
The statistic which will now come into focus for Benfica is instead a 52 year wait to win a European title when they contest the final next month. Jorge Jesus's side will return to Turin intent on making the place a home away from home again - the Portuguese having restricted Juventus to a handful of chances last night.
Dani Osvaldo tapped the ball into the net following Paul Pogba's headed knockdown, only for officials to flag for offside against the Frenchman.