Trailing 2-1 from last week’s first leg, Bilbao got back on level terms after just 17 minutes through Markel Susaeta, who shot into the roof of the net after being set up by Llorente. Sporting then got their noses back in front two minutes before the break when Ricky van Wolfswinkel fired home from inside the box, yet it lasted two minutes as Ibai Gomez slid the ball past Rui Patricio following a superb drag-back and pass from Llorente.
There was more drama to come in the second half as both teams hit the woodwork, Javi Martinez seeing a header strike an upright for Athletic before Emiliano Insua drilled a deflected low shot against the outside of a post.
Nonetheless, with it looking increasingly like extra-time would be needed to separate the sides, Llorente poked the ball home from close range two minutes from time to give the Basques a 4-3 aggregate victory and send them into their first European final for 35 years.
Bilbao boss Marcelo Bielsa said he felt “great joy” for his players and “relief” for the fans after he was able to give them what they wanted.
“I am very happy for my players, for whom I feel great joy, because it was a tremendous effort and they showed great commitment. I have congratulated them and told them they absolutely deserved this.
“For the fans these type of games create a great stir and it’s our responsibility to bring them some happiness, although there is also the fear of disappointment. So it is a relief,” he added.
Opposite number Ricardo Sa Pinto believed his side’s exit was “unjust” and insisted he was proud of his players.
“I think the result was unjust but that is how it is,” he lamented. “The third goal decided a tie that was finely balanced. It is hard to take for players who have been fantastic, given everything, and who 95 per cent of people thought wouldn’t get this far.
“I am very proud of them because they have been courageous and brave, but the goal we conceded in the first leg was what allowed Athletic to make it through to the final.”
Athletic Bilbao 3-1 Sporting Lisbon
Scorers: Susaeta 17, Ibai Gomez 45, Llorente 88 (BIL), Van Wolfswinkel 43 (SPO)
Athletic Bilbao: Iraizoz; Iraola, Javi Mart