Recruiters and job seekers rely on search systems to navigate labor markets, making candidate matching engines critical for hiring outcomes. Most systems act as keyword filters, failing to handle skill synonyms and nonlinear careers, resulting in missed candidates and opaque match scores. We introduce JobMatchAI, a production-ready system integrating Transformer embeddings, skill knowledge graphs, and interpretable reranking. Our system optimizes utility across skill fit, experience, location, salary, and company preferences, providing factor-wise explanations through resume-driven search workflows. We release JobSearch-XS benchmark and a hybrid retrieval stack combining BM25, knowledge graph and semantic components to evaluate skill generalization. We assess system performance on JobSearch-XS across retrieval tasks, provide a demo video, a hosted website and installable package.