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Large language models (LLMs) encode vast amounts of world knowledge but remain static once trained, making timely integration of emerging facts prohibitively expensive via full retraining. Knowledge-editing techniques have thus emerged to inject or overwrite specific facts into LLMs, yet they either over-rely on superficial cues or incur complex, iterative pipelines that collapse under noisy, multi-hop conditions. We introduce **Reason-KE**, an end-to-end reasoning-chain-based editing framework that steers a pretrained LLM through four structured stages—fact acknowledgment, relevance determination, selective application, and final reasoning—to filter distractors in a single pass. Trained on MQuAKE-CF with up to four irrelevant facts, Reason-KE elevates Qwen2.5-7B’s multi-hop QA accuracy to 90.2% (↑17.6 pp) while suffering merely 6.3% drop under heavy distraction and <1% when answers are leaked. Our quantitative analysis confirms Reason-KE’s resilience and efficiency, establishing a new state of the art for reliable LLM knowledge updates. The code will be released.