Having made a bright start to the match, Bilbao broke the deadlock in the 13th minute. Ibai Gomez sent over a cross for Llorente, who planted a header into the net from six yards out.
Gomez almost made it two before the break when his powerful strike hit the side netting.
Bilbao continued to dominate the contest after the restart but they were unable to add to their tally further.
The victory has lifted Bilbao up to eighth in the La Liga table.