Sevilla entered the match as the strong favourites to advance following a 2-0 victory in the first leg last week.
The home side completed the turnaround 20 minutes from time when Jeremy Mathieu converted from close range.
There was to be late drama, however, with Stephane Mbia's late header seeing Sevilla advance to the final on away goals.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary of the action below.
VALENCIA: Alves; Joao, R. Costa, Mathieu, Bernat; Parejo, Keita; Feghouli, Vargas, Piatti; Jonas
SEVILLA: Beto; Coke, Pareja, Fazio, Navarro; Mbia, Carrico; Vitolo, Rakitic, Reyes; Bacca
Los aficionados del Sevilla, en las gradas de Mestalla pic.twitter.com/7bjGYVk6KV— MARCA (@marca) May 1, 2014