Artificial intelligence is increasingly embedded in accounting, auditing, and fraud-detection systems, yet existing research remains fragmented between studies emphasizing algorithmic performance and those examining professional, organizational, ethical, and regulatory conditions. This systematic literature review synthesizes 37 studies published between 2020 and 2025 and indexed in Scopus, Web of Science, and ScienceDirect to explain how, why, and under what conditions AI capability translates into trustworthy financial-control outcomes. Guided by PRISMA 2020 and a theory-building thematic synthesis, the review integrates evidence on machine learning, deep learning, natural language processing, explainable AI, big data analytics, blockchain-enabled systems, and related digital technologies. The synthesis reveals that AI consistently strengthens transaction-level fraud detection, anomaly identification, audit analytics, and selected financial-reporting functions; however, technical performance alone does not ensure organizational effectiveness. Human professional capability, explainability, transparency, trust, cybersecurity maturity, organizational readiness, and regulatory governance emerge as critical mechanisms and boundary conditions. The evidence further reveals a digital fraud paradox in which the same technologies that strengthen detection may simultaneously increase the sophistication and adaptability of fraudulent behavior. Integrating Socio-Technical Systems Theory, the Technology–Organization–Environment framework, and responsible AI perspectives, this review develops a multi-level framework in which trusted financial integrity results from the alignment of technical capability, human judgment, responsible governance, and institutional readiness. The study advances the literature beyond algorithm comparison toward a conditional and socio-technical explanation of responsible AI-enabled financial control.