Electrical control of spins at the nanoscale offers significant architectural advantages in spintronics, because electric fields can be confined over shorter length scales than magnetic fields. Thus, recent demonstrations of electric-field sensitivities in molecular spin materials are tantalizing, raising the viability of the quantum analogues of macroscopic magneto-electric devices. However, the electric-field sensitivities reported so far are rather weak, prompting the question of how to design molecules with stronger spin-electric couplings. Here we show that one path is to identify an energy scale in the spin spectrum that is associated with a structural degree of freedom with a substantial electrical polarizability. We study an example of a molecular nanomagnet in which a small structural distortion establishes clock transitions (that is, transitions whose energy is to first order independent of the magnetic field) in the spin spectrum; the fact that this distortion is associated with an electric dipole allows us to control the clock-transition energy to an unprecedented degree. We demonstrate coherent electrical control of the quantum spin state and exploit it to independently manipulate the two magnetically identical but inversion-related molecules in the unit cell of the crystal. Our findings pave the way for the use of molecular spins in quantum technologies and spintronics.