Path-sensitive vulnerabilities, such as use-after-free, integer overflows, and command injection, pose significant challenges for traditional static analysis tools, which often face trade-offs between precision, scalability, and interpretability. To address these challenges, we present SEVDF (Semantic-Enhanced Vulnerability Detection Framework), a novel methodology that integrates may-analysis taint propagation with large language models (LLMs) to detect path-related vulnerabilities in large C/C++ codebases. SEVDF begins by constructing a program dependency graph and performing a sound but incomplete taint analysis to extract all potential vulnerable paths. After segmentation, deduplication, feasibility check, and semantic summarization by LLMs, the vulnerable paths are reformed and confirmed with LLMs for their inter-procedural feasibility and semantic consistency. We evaluate SEVDF on the Juliet Test Suite (thirteen CWE categories) and a curated real-world dataset of 71 vulnerabilities across 9 projects. SEVDF consistently outperforms the default CodeQL rules, CodeQL rules with all unnecessary constraints removed, and three open-source detectors, which are Infer, Cppcheck and CodeChecker. SEVDF is able to achieve 100% precision on several CWEs while maintaining or improving recall on Juliet benchmark. Moreover, our segment-based design reduces the analysis workload for LLMs by 90.6% compared to direct-path prompting through Logic Unit deduplication, making SEVDF cost-effective for large-scale deployment. Finally, SEVDF uncovered and reported 29 0-day vulnerabilities (12 confirmed to date), including 3 CVEs in VirtualBox, demonstrating practical value.