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Periodically driven quantum systems suffer from heating via resonant excitation. While such Floquet heating guides a generic isolated system towards the infinite-temperature state, a driven open system, coupled to a thermal bath, will approach a non-equilibrium steady state. We show that the interplay of bath-induced dissipation and controlled Floquet heating can give rise to non-equilibrium Bose condensation in a mode protected from Floquet heating. In particular, we consider a one-dimensional (1D) Bose gas in an optical lattice of finite extent, which is coupled weakly to a three-dimensional thermal bath given by a second atomic species. The bath temperature $T$ lies well above the crossover temperature, below which the majority of the system's particles form a (finite-size) Bose condensate in the ground state. However, when a strong local potential modulation is switched on, which resonantly excites the system, a non-equilibrium Bose condensate is formed in a state that decouples from the drive. Our predictions, which are based on a microscopic model that is solved using kinetic equations of motion derived from Floquet-Born-Markov theory, can be probed under realistic experimental conditions.