Large Language Models (LLMs) suffer from hallucinations, severely undermining their reliability. While white-box hallucination detection methods that leverage hidden states prevail, they fail to identify and focus on fact-critical information when analyzing token sequences. To address this, we propose LAFaCT, a Localize-then-Analyze detection framework. It first localizes fact-critical tokens using Factual Criticality, a novel metric derived from feature attribution. A subsequent stage then performs a focused sequential analysis on their hidden states. Extensive experiments on eight benchmarks and multiple model families confirm LAFaCT as the new state-of-the-art, with in-depth analyses validating the effectiveness of its core token-localization strategy.