It was the away side who started the better and Oscar De Marcos so nearly found the opener after nine minutes, but his attempt was blocked.
Chances remained few and far between in the latter stages of the half with an Adrian strike for Racing five minutes before the interval their best chance of the opening period.
Toquero had a golden chance to grab Bilbao's second after 50 minutes, but he was denied, before Ander struck wide from close range moments later.
Bilbao again came close via Ibai Gomez just before the 60-minute mark, but his effort was blocked by the Racing defence.
Racing's best chance of the second period fell to Domingo Cisma after 66 minutes, but he just dragged wide when he might have done better.
Bilbao held on for the win, however, to aid their push for European football, while Racing remain in deep relegation trouble.