Resource leaks pose a persistent threat to software reliability, resulting in resource exhaustion, performance degradation, and system crashes. Existing automated repair approaches, primarily based on rigid templates, are limited in handling complex or multi-resource leak scenarios and often compromise program semantics. Although recent advances in Large language models show promise in program repair, existing LLM-based methods frequently generate semantically invalid patches for resource leaks. This paper presents \textit{Amur}, a semantics-aware patching framework that leverages static analysis to guide LLMs in repairing both single- and multi-resource leaks. At the core of Amur is a novel \textit{Resource Flow Analysis (RFA)}, a flow-sensitive and inter-resource-aware static analysis that captures resource usage patterns and dependencies. RFA identifies potential leak points and enforces semantic constraints to guide LLMs in synthesizing semantics-preserving patches. We evaluate Amur on the NJR-1 dataset and the new \textbf{JLeaks} benchmark (ICSE 2024), which targets realistic multi-resource leak scenarios. Amur achieves substantial improvements over state-of-the-art methods, improving patch accuracy by 33% over RLFixer and 24% over LLM-only baselines in single-resource leak cases. For multi-resource leaks, Amur generates patches in 96% of cases and achieves 80% correctness, outperforming RLFixer and LLM-only baselines by 76% and 16%, respectively. These results demonstrate that integrating RFA into LLM-guided repair significantly enhances the correctness and generalizability of automated resource leak fixes.