Topological operations can achieve certain goals without requiring accurate control over local operational details; for example, they have been used to control geometric phases and have been proposed as a way of controlling the state of certain systems within their degenerate subspaces. More recently, it was predicted that topological operations can be used to transfer energy between normal modes, provided that the system possesses a specific type of degeneracy known as an exceptional point. Here we demonstrate the transfer of energy between two vibrational modes of a cryogenic optomechanical device using topological operations. We show that this transfer arises from the presence of an exceptional point in the spectrum of the device. We also show that this transfer is non-reciprocal. These results open up new directions in system control; they also open up the possibility of exploring other dynamical effects related to exceptional points, including the behaviour of thermal and quantum fluctuations in their vicinity.