The game had been postponed last week due to security concerns in the Israeli city where Kiryat Shmona are playing their Europe League ties, but last year's finalists coped with the disruption well and went ahead 11 minutes before half-time when Llorente tapped home from close range.
And Toquero sealed the win 15 minutes from time with his second goal of the season to ensure the Basques will not suffer the ignominy of finishing last in Group I.
Sparta Prague's draw with Lyon last week meant both sides had already been eliminated and Marcelo Bielsa took the opportunity to give a number of his younger players a game, with Llorente the only man retained from Sunday's 1-1 Primera Division draw with Deportivo La Coruna.
Indeed, among those making their debut was Aymeric Laporte - who becomes only the second foreign player to start for Athletic after former French international Bixente Lizarazu.
It was Llorente though who was the protagonist in the first half as his power proved too much for the Kiryat defence to deal with.
The Spanish international saw one long-range effort come back off the crossbar, whilst the hosts' goalkeeper Daniel Amos also denied him twice and made smart saves from Alvaro Pena on a couple of occasions.
Toquero was next to test the Israeli with a fierce volley from outside the area that he parried to safety, but eventually his side's luck ran out as after he again denied Toquero with a brave low save - but the ball fell for Llorente to stroke home only his second goal of the season.
Other than a Sintayehu Sallalich goal that had been rightly ruled out for offside, the hosts had offered very little as an attacking threat in the first half - but they were nearly level just four minutes after the break as Sallalich picked out Darko Tasevski and his strike forced a good save from Raul Fernandez.
However, the introduction of Ibai Gomez with 25 minutes to go gave the visitors the extra dimension in the final third needed to kill the game off. The winger went close himself with a left-footed shot which whistled past the post before teeing up Llorente, whose fine header brought another good save out of Amos.
The second goal arrived soon after though as Ibai's free-kick was blocked - but the ball fell kindly for Toquero to slide it past Amos and at least salvage some pride for Athletic from what has been a disappointing European campaign.