If you took the Earth and spun it up, you would expect it to go oblate (bulge outwards) along the equator. Similarly, the gravitational fiedl would also become oblate, because the mass in the bulge attracts to itself. The Earth, at the rate it is spinning actually is oblate, and the gravitational field follows along. It is the asymmetry in the field that cases the Earth to slowly exchange rotational momentum with the moon, slowing the Earth's spin and moving the moon's orbit further out.
There is no difference between this model of Earth and a black hole mass. The mass is mysterious only because we cannot see it; there is no reason to suppose it doesn't act in the same way, though the speeds may begin making relativistic effects apparent, just as Mercury orbiting the Sun is not perfectly classical.
This would also apply to binary systems. Picture two sub-black hole stars rotating around each other and how they are distorted by each other's gravitational fields. Black holes would react the same way, barring the relatavistic effects.