Markel Susaeta opened the scoring for Athletic Bilbao on the night after 17 minutes before Ricky van Wolfswinkel hit back one minute before half-time.
But Ibai Gomez put the hosts back in front just 60 seconds later to leave the tie level on aggregate at half-time before, with extra-time beckoning, Llorente struck to set up a clash with Liga rivals Atletico Madrid in the final.
The tie was delicately poised going into the second leg after Sporting's 2-1 victory in the opening game, with Emiliano Insua and Diego Capel scoring within four minutes of each other to cancel out Jon Aurtenetxe's opener at the Estadio Jose Alvalade.
Bielsa's men play an exciting, attacking brand of football and the home side took the lead in fine fashion, with a well-crafted move which saw Iker Muniain cross from the right to Llorente, who chested the ball to Susaeta to dispatch a volley into the ground and past Rui Patricio.
The visitors, who knocked out Manchester City in the last 16, looked to hit back quickly and Capel's cross was met by Bruno Pereirinha but the 24-year-old put his free header over the crossbar.
Gomez thought he has extended Athletic Bilbao's lead on the half-hour but had strayed offside before planting a header beyond Patricio, while Gomez went close once again when Andoni Iraola swung in a pinpoint cross from the right and the 22-year-old failed to make contact with only the goalkeeper to beat.
The hosts continued to ramp up the pressure and Llorente forced a smart stop from Patricio before Sporting Lisbon hit back, with Van Wolfswinkel firing a low shot from the edge of the box past the outstretched Gorka Iraizoz after Athletic Bilbao failed to properly clear a corner.
But Athletic, who are yet to taste European glory, needed less than a minute to re-establish their lead on the night, with Llorente producing a sublime piece of skill to play in Gomez, who made no mistake in beating Patricio to leave the tie on a knife-edge at 3-3 on aggregate going into the break.
Bielsa's side continued to create the better chances after the restart and Susaeta unleashed a powerful shot from the top-right corner of the box to test Patricio's reactions.
Fernando Amorebieta then sent his header crashing against the post while Sporting also hit the woodwork when Insua let fly with a fierce shot which skidded off the surface, took a deflection and hit the outside of the upright with 35 minutes remaining
Both sides continued to press but failed to create a meaningful chance and the game looked set to go to extra-time until Andre Martins chipped in a deep cross for Gomez, who turned to work a yard of space before firing a low shot goalwards which Llorente directed into the back of the net.