In deployed large language models (LLMs), inference energy consumption has grown rapidly and has emerged as a key bottleneck in large-scale deployment, yet most existing inference efficiency methods focus on reducing FLOPs or latency, rather than explicitly modeling or enforcing end-to-end inference energy constraints. We propose EOP-LLM, an energy-oriented dynamic pruning framework that enables LLM inference under explicit per-sequence energy budgets. EOP-LLM combines a device-calibrated energy proxy with lightweight token and feed-forward (FFN) selectors, coordinated through a global dual variable, to dynamically allocate computation while preserving model quality. Extensive experiments on LLaMA 3.2 (1B/3B) and LLaMA 3.1 (8B) demonstrate that EOP-LLM consistently outperforms state-of-the-art dynamic pruning baselines under matched energy budgets, while strictly adhering to per-sequence energy constraints.