The 1-1 draw means that Deportivo remain just two points clear of the relegation zone in La Liga, while the visitors stay in 14th place.
It was Deportivo who took the lead, though, when five minutes from the break, Bruno Gama found space just outside the box and fired the ball into the top corner.
There was still time for the away side to equalise on the stroke of half time when Andoni Iraola's chip was met by Llorente, who placed his header into the bottom corner.
In the second period, Bilbao pushed hard for a winner as both Muniain and Llorente were again denied by Aranzubia.
With 10 minutes to go, though, the visitors were reduced to 10 men, when Ander Iturraspe earned his second yellow card of the evening for a late tackle.
Gama missed the chance to double his tally and take all three points for Deportivo, slicing his shot high and wide from the edge of the box in the final five minutes, and the points were shared.