Applying large language models (LLMs) to RTL code optimization for improved power, performance, and area (PPA) faces two key challenges: ensuring functional correctness of optimized designs despite LLM hallucination, and systematically prioritizing power reduction within the multi-objective PPA trade-off space. We propose POET (Power-Oriented Evolutionary Tuning), a framework that addresses both challenges. For functional correctness, POET introduces a differential-testing-based testbench generation pipeline that treats the original design as a functional oracle, using deterministic simulation to produce golden references and eliminating LLM hallucination from the verification process. For PPA optimization, POET employs an LLM-driven evolutionary mechanism with non-dominated sorting, power-first intra-level ranking, and proportional survivor selection to steer the search toward the low-power region of the Pareto front without manual weight tuning. Evaluated on the RTL-OPT benchmark across 40 diverse RTL designs, POET achieves 100% functional correctness, the best power on all 40 designs, and competitive area and delay improvements.

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