Marcelo Bielsa's men, who accounted for Manchester United early in the competition, looked set to take the tie into extra-time after goals from Markel Susaete and Gomez Ibai sandwiched a strike from Rene van Wolfswinkel at the Estadio San Mames.
But with the score at 2-1 to Athletic on Thursday night and 3-3 on aggregate, Llorente lashed a right-foot shot into the corner of the net from an Ibai cross to seal the home side's passage into the final where they will meet fellow Spaniards Atletico Madrid.
Conscious that an early goal for Sporting could spell the end of their chances, the home side started nervously and Matias Fernandez fired a free-kick over the bar for the visitors in the seventh minute.
Llorente brought the first save out of Sporting keeper Rui Patricio in the ninth minute with a left-foot shot, then Iker Muniain saw his effort from six yards blocked by Sporting's Alexandre Xandao.
Patricio saved from Ibai as Bilbao began to press, but the hosts' pressure finally told in the 17th minute when Susaeta rifled a left-foot shot high into the net after a short pass from Llorente.
Sporting almost responded through Fernandez, who had a shot blocked in the net, while Bruno Pereirinha should have done better from close quarters, before Brazilian Anderson Polga forced a fingertip save out of home keeper Gorka Iraizoz.
The home side had chances of their own with Patricio tipping a Llorente effort round the post, before Sporting put themselves back in control of the tie two minutes before the break when Van Wolfswinkel fired home from the centre of the box.
The visitors' lead lasted less than three minutes as Athletic Club levelled the aggregate scores three minutes later when Ibai drilled a low shot past Patricio after being set up by the ever-present Llorente.
In an exciting start to the second half, Patricio tipped over a shot from Susaeta and a Llorente header hit the post, before Emiliano Insua came close at the other end with a drilled shot which Iraizoz tipped round the post.
Polga's long-range effort was easily held by Iraizoz and the game looked to be heading for extra-time when Ibai crossed from the left side of the penalty area and Llorente fired home to send Bilbao to the final.