Magnetic nanorods rotating in a viscous liquid are very sensitive to any ambient magnetic field. We theoretically predicted and experimentally validated the conditions for two-dimensional synchronous and asynchronous rotation as well as three-dimensional precession and tumbling of nanorods in an ambient field superimposed on a planar rotating magnetic field. We discovered that any ambient field stabilizes the synchronous precession of the nanorod so that the nanorod precession can be completely controlled. This effect opens up different applications of magnetic nanorods as sensors of weak magnetic fields, for microrheology, and generally for magnetic levitation.