Nature has developed methods for controlling the movements of organisms with many degrees of freedom which differ strongly from existing approaches for balance control in humanoid robots: Biological organisms employ kinematic synergies that simultaneously engage many joints, and which are apparently designed in such a way that their superposition is approximately linear. We show in this article that this control strategy can in principle also be applied to balance control of humanoid robots. In contrast to existing approaches, this control strategy reduces the need to carry out complex computations in real time (replacing the iterated solution of quadratic optimization problems by a simple linear controller), and it does not require knowledge of a dynamic model of the robot. Therefore it can handle unforeseen changes in the dynamics of the robot that may for example arise from wind or other external forces. We demonstrate the feasibility of this novel approach to humanoid balance control through simulations of the humanoid robot HOAP-2 for tasks that require balance control on a randomly moving surfboard.