The number and heterogeneity of compute devices, even within a single compute node, has been steadily on the rise. Since all systems must operate under a power cap, the number of discrete devices that can run simultaneously at their highest frequency is limited by the globally-imposed power cap. Current systems incorporate a centralized power management unit that statically controls the distribution of power among the devices within the node. However, such static distribution policies are unaware of the dynamic utilization profile across the devices, which leads to unfair power allocations that end up degrading system throughput performance. The problem is particularly acute in the presence of heterogeneity since type-specific performance-boost capabilities cannot be leveraged via utilization-agnostic static power allocations. This paper proposes Adaptive Power Shifting for multi-accelerator heterogeneous systems (APS), a technique that leverages system utilization information to dynamically allocate and re-distribute power budgets across multiple discrete devices. Democratizing the power allocation based on dynamic needs results in dramatic speedup over a need-agnostic static allocation. We use APS in a real OpenPOWER compute node with 2 CPUs and 4 GPUs to demonstrate the value of on-demand, equitable power allocations. Overall, the proposed solution increases performance with respect to two state-of-the-art techniques by up to 14.9% and 13.8%.