The efficient conversion of thermal energy to mechanical work by a heat engine is an ongoing technological challenge. Since the pioneering work of Carnot, it is known that the efficiency of heat engines is bounded by a fundamental upper limit, the Carnot limit. Theoretical studies suggest that heat engines may be operated beyond the Carnot limit by exploiting stationary, non-equilibrium reservoirs that are characterized by a temperature as well as further parameters. In a proof-of-principle experiment, we demonstrate that the efficiency of a nano-beam heat engine coupled to squeezed thermal noise is not bounded by the standard Carnot limit. Remarkably, we also show that it is possible to design a cyclic process that allows for extraction of mechanical work from a single squeezed thermal reservoir. Our results demonstrate a qualitatively new regime of non-equilibrium thermodynamics at small scales and provide a new perspective on the design of efficient, highly miniaturized engines.