Run-time resource management of heterogeneous multi-core systems is challenging due to i) dynamic workloads, that often result in ii) conflicting knob actuation decisions, which potentially iii) compromise on performance for thermal safety. We present a run-time resource management strategy for performance guarantees under power constraints using functionally approximate kernels that exploit accuracy-performance trade-offs within error resilient applications. Our controller integrates approximation with power knobs - DVFS, CPU quota, task migration - in coordinated manner to make performance-aware decisions on power management under variable workloads. Experimental results on Odroid XU3 show the effectiveness of this strategy in meeting performance requirements without power violations compared to existing solutions.