Bloch band theory and bulk-boundary correspondence in non-Hermitian systems are attracting great attention in different areas of science. Interband transitions and Rabi flopping induced by emission or absorption of field quanta are fundamental and well-understood processes in Hermitian systems. However, they are challenged in a non-Hermitian system, where band theory is affected by system boundaries. Here we consider Rabi oscillations in non-Hermitian lattices exhibiting unbalanced non-Hermitian skin effect, and unveil an unprecedented scenario of Rabi flopping. The effective dipole moment of the transition - usually considered a bulk property - is however strongly dependent on boundary conditions. Rabi oscillations become anharmonic and transitions cease to be vertical in the energymomentum plane in systems with open boundaries. Remaining stable even in the presence of complex energies, Rabi oscillations provide a vivid illustration of how competition between non-Hermitian, non-local and Floquet effects can result in significant enhancements of physically measurable quantities