Dynamically configuring algorithm hyperparameters is a fundamental challenge in computational intelligence. While learning-based methods offer automation, they suffer from prohibitive sample complexity and poor generalization. We introduce AutoEP, a novel framework that bypasses training entirely by leveraging Large Language Models (LLMs) as zero-shot reasoning engines for algorithm control. AutoEP's core innovation lies in a tight synergy between two components: (1) an online Exploratory Landscape Analysis (ELA) module that provides real-time, quantitative feedback on the search dynamics, and (2) a multi-LLM reasoning chain that interprets this feedback to generate adaptive hyperparameter strategies. This approach grounds high-level reasoning in empirical data, mitigating hallucination. Evaluated on three distinct metaheuristics across diverse combinatorial optimization benchmarks, AutoEP consistently outperforms state-of-the-art tuners, including neural evolution and other LLM-based methods. Notably, our framework enables open-source models like Qwen3-30B to match the performance of GPT-4, demonstrating a powerful and accessible new paradigm for automated hyperparameter design. Our code is available at https://github.com/YiZheZhang12/AutoEP.