Bilbao back to winning ways in La Liga
The Spain international struck the bar when presented with an open goal in the first half while Alvaro Negredo had an effort cleared off the line for the visitors.
But Llorente made amends for his earlier miss when he bulleted home Markel Susaeta's cross two minutes into the second half.
Mikel San Jose struck the post following a wonderful run by Iker Muniain as Athletic struggled to put the game to bed, but they held on to move within two points of Osasuna in the final Europa League spot.
The match had been billed as a showdown between Llorente and Negredo in the battle for a place in the Spain side for Euro 2012 and both should have scored in the first half.
The Sevilla striker was first to threaten when Gorka Iraizoz spilled Manu del Moral's shot but his clever lob was cleared off the line by Fernando Amorebieta.
Andres Palop then produced a brave stop as he dived to smother Llorente's effort from close range and Athletic's top scorer came even closer 10 minutes later when a lovely Jon Aurtenetxe cross left Palop stranded but Llorente could not control his shot on the stretch and the ball came back off the bar.
Negredo had another clear sight of goal 12 minutes before the break as Borja Ekiza's slip allowed him in but he wastefully fired high over the bar.
The hosts made the breakthrough just after half-time as a patient build-up involving Muniain and Susaeta found Llorente in the area and he showed great strength to power his header high past Palop.
Negredo continued to be Sevilla's main threat as his left-footed drive from outside the area skidded just wide and he then rounded Iraizoz after a great through ball from Antonio Luna but the angle was too tight and his effort hit the side-netting.
In Sevilla's attempts to get an equaliser they were leaving huge gaps for Athletic to exploit and Susaeta should have done better when clean through with 15 minutes remaining but his lob was easily handled by Palop.
The hosts came even closer to sealing the points on 87 minutes. After wonderful jinking run past three Sevilla defenders, Muniain picked out San Jose at the back post but he could only power his shot against the outside of the post.