The proliferation of deceptive content online necessitates robust Fake News Detection (FND) systems. While evidence-based approaches leverage external knowledge to verify claims, existing methods face critical limitations: noisy evidence selection, generalization bottlenecks, and unclear decision-making processes. Recent efforts to harness Large Language Models (LLMs) for FND introduce new challenges, including hallucinated rationales and conclusion bias. To address these issues, we propose \textbf{RoE-FND} (\textbf{\underline{R}}eason \textbf{\underline{o}}n \textbf{\underline{E}}xperiences FND), a framework that reframes evidence-based FND as a logical deduction task by synergizing LLMs with experiential learning. RoE-FND encompasses two stages: (1) \textit{self-reflective knowledge building}, where a knowledge base is curated by analyzing past reasoning errors, namely the exploration stage, and (2) \textit{dynamic criterion retrieval}, which synthesizes task-specific reasoning guidelines from historical cases as experiences during deployment. It further cross-checks rationales against internal experience through a devised dual-channel procedure. Key contributions include: a case-based reasoning framework for FND that addresses multiple existing challenges, a training-free approach enabling adaptation to evolving situations, and empirical validation of the framework's superior generalization and effectiveness over state-of-the-art methods across three datasets.