Sevilla had a golden chance to take the lead in the sixth minute when former Celta midfielder Michael Krohn-Dehli showed excellent feet inside the box before attempting to squeeze one past Ruben Blanco at the near post, but the Dane hit the side-netting.
Guidetti proved Celta's biggest threat in the opening 15 minutes of action, with the powerful striker causing Sevilla's backline problems due to his pace and power in the final third.
Coke and Kevin Gameiro both had half-chances for the visitors inside the opening 30 minutes, but despite both sides committing numbers in the final third, clear opportunities were very much at a premium.
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Celta's first real chance arrived in the 30th minute when Aspas found space inside the Sevilla box, but the Spaniard could not beat Sergio Rico from a tight angle, before Daniel Wass headed over the Sevilla crossbar moments later.
The hosts were ahead on the night in the 35th minute, however, when Aspas converted a low Fabian Orellana cross at the far post, which cut the aggregate score to 4-1.
Sevilla should have levelled the scores in the latter stages of the first period when Vicente Iborra rose above everyone inside the Celta box, but his header crashed off the outside of the post.
Iborra's aerial presence brought the first half-chance of the second period, but this time the Spaniard missed the target completely as Celta survived what would have been a killer goal.
Celta had two excellent chances in the 50th minute to take a 2-0 lead on the night, but Guidetti saw his close-range header kept out by Rico, before Aspas somehow headed wide of the post from close range.
Sevilla were wobbling at the back as the second leg approached the hour, with a series of high balls into the box causing all sorts of problems to Unai Emery's side.
Indeed, Celta had their second in the 55th minute when Aspas headed home from close range after Rico parried a low cross from Wass. Less than two minutes later, however, Sevilla scored a vital away goal through Banega to silence what was a growing atmosphere inside the stadium.
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During an incredible period, Celta were then awarded a controversial penalty when Guidetti went down inside the box under a challenge from Rico, but the striker could only hit the post with his spot kick.
Banega and Orellana had chances at either end as the match headed for its final 20 minutes, but neither could find the target from distance as it remained 2-1 Celta on the night and 5-2 Sevilla on aggregate.
Rico was again called into action in the 78th minute to keep out a swinging drive from Orellana, before Pablo Hernandez missed the target as Celta continued to search for a third goal.
It was Sevilla that had the last laugh, however, as Vitolo set up Konoplyanka in the 87th minute to deny Celta a win on the night and secure a 6-2 aggregate success for the visitors, who will meet Barcelona in the final.