Energy transfer plays a vital role in many natural and technological processes. In this work, we study the effects of mechanical motion on the excitation transfer through a chain of interacting molecules with applications to biological scenarios of transfer processes. Our investigation demonstrates that, for various types of mechanical oscillations, the transfer efficiency is significantly enhanced over that of comparable static configurations. This enhancement is a genuine quantum signature and requires the collaborative interplay between the quantum-coherent evolution of the excitation and the mechanical motion of the molecules; it has no analogue in the classical incoherent energy transfer. This effect may not only occur naturally but also be exploited in artificially designed systems to optimize transport processes. As an application, we discuss a simple and hence robust control technique.