Large language model (LLM) safety classifiers such as Llama Guard are effective at detecting overtly harmful prompts but remain vulnerable to adversarial jailbreak attacks that disguise malicious intent through role-play scenarios, fictional framing, and indirect requests. We present Reflect-Guard, a method that augments LLM-based safety classifiers with chain-of-thought self-reflection capabilities through parameter-efficient fine-tuning. Our approach distills analytical reasoning from GPT-4o-mini into structured reflection annotations, then trains Llama-Guard-3-8B via QLoRA to generate logical self-reflections before issuing safety verdicts. Using only 1000 training examples and updating just 0.5% of model parameters (~42M), Reflect-Guard achieves substantial improvements on two challenging benchmarks. On WildGuardTest, F1 score improves from 0.770 to 0.842 (+7.2 pp), with recall on adversarial prompts increasing from 0.513 to 0.921 (+40.8 pp). On JailbreakBench, the attack success rate drops from 10.3% to 1.8%, representing an 82.5% relative reduction. These gains are especially pronounced on adversarial inputs, where the explicit reasoning step enables the model to see through obfuscation techniques that defeat standard pattern-matching approaches. Our results demonstrate that teaching safety classifiers to reason about adversarial intent, rather than simply classify surface patterns, is a promising direction for robust LLM safety.