We demonstrate spatial Rabi oscillations in optical waveguide arrays. Adiabatic transitions between extended Floquet-Bloch modes associated with different bands are stimulated by periodic modulation of the photonic lattice in the propagation direction. When the stimulating modulation also carries transverse momentum, the transition becomes indirect, equivalent to phonon-assisted Rabi oscillations. In solid state physics such indirect Rabi oscillations necessitate coherent phonons and hence they have never been observed. Our experiments suggest that phonon-assisted Rabi oscillations are observable also with Bose-Einstein condensates, as well as with other wave systems-where coherence can be maintained for at least one period of the Rabi oscillation.