Aritz Aduriz nodded Bilbao ahead in the 67th minute and Granada, fifth from bottom on 28 points, almost snatched an equaliser in the first minute of added time when midfielder Yacine Brahimi crashed a shot against the post.
Bilbao, who along with Real Madrid and Barcelona have never suffered relegation from the top flight, have been a shadow of the team that reached the final of the Europa League and the Copa del Rey last season.
Aritz Aduriz was on the pitch for 79 minutes against Granada CF. The striker scored in the 67th minute and took four shots.
Los Rojiblancos are in 13th place with a record of 10 wins, 14 losses and five draws.
Granada CF have a record of seven wins, 15 losses and seven draws this season, which puts them in 16th place, only one point above the relegation zone.
Athletic Bilbao controlled possession for 54.4% of the contest thanks to strong open field play.
Los Leones got off nine shots, including four on target, during the match, a direct result of their 79 duels and 17 headers won.
Iker Muniain went off due to injury in the 90th minute and was replaced by Gaizka Toquero.
Granada CF had 45.6% of the possession during the match.
Granada CF had seven shots, including three on target.
The two attempts by Yacine Brahimi were the most of any Granada CF player.
The combination of Mikel Rico to Brayan Angulo was the most common during the match, as the two players connected 15 times.