Large language models (LLMs) have demonstrated impressive capabilities across diverse tasks, but they remain susceptible to hallucinations--generating content that appears plausible but contains factual inaccuracies. We present Finch-Zk, a black-box framework that leverages fine-grained cross-model consistency to detect and mitigate hallucinations in LLM outputs without requiring external knowledge sources. Finch-Zk introduces two key innovations: 1) a cross-model consistency checking strategy that reveals fine-grained inaccuracies by comparing responses generated by diverse models from semantically-equivalent prompts, and 2) a targeted mitigation technique that applies precise corrections to problematic segments while preserving accurate content. Experiments on the FELM dataset show Finch-Zk improves hallucination detection F1 scores by 6-39\% compared to existing approaches. For mitigation, Finch-Zk achieves up to 9 absolute percentage points improvement in answer accuracy on the GPQA-diamond dataset when applied to state-of-the-art models like Llama 4 Maverick and Claude 4 Sonnet. Extensive evaluation on multiple datasets demonstrates that Finch-Zk provides a practical, deployment-ready safeguard for enhancing factual reliability in production LLM systems.