The first clear chance of the match feel to the visitors just before the half-hour mark. Brayan Angulo's cross was met by the head of Nolito, but his effort was expertly tipped onto the crossbar by Iraizoz.
Bilbao had to wait until the 64th minute for their first good sight of goal, and they should have opened the scoring with it. Ibai Gomez picked up a loose ball in the area but could only steer his effort wide.
The hosts did take the lead shortly afterwards, however, when Gomez's ball into the box was met by a thumping header courtesy of Aritz Aduriz, who netted his 17th goal of the season.
Granada's chances of finding an equaliser took a positive turn with just seven minutes left when Markel Susaeta put in a poor tackle on Nolito to earn his second yellow card.
The visitors poured forward in the closing stages in search of an equaliser and came within inches of getting it when Yacine Brahimi tried an effort from range, only to see it bounce back off the post as the hosts held out for all three points.