Workplaces everywhere are changing fast, and nowhere is that change more visible than in how organizations try to keep their people engaged. This paper explores a question that sits at the heart of modern HR management: does organizational culture influence how engaged employees feel at work — and does artificial intelligence play a role in connecting the two? Drawing on a systematic review of 51 peer-reviewed studies published between 2017 and 2026, filtered through the PRISMA framework and analyzed using Biblioshiny-based bibliometric mapping, this study synthesizes a rapidly expanding body of literature that spans management, organizational behaviour, and information systems. Three theoretical frameworks anchor the analysis: Kahn's (1990) psychological conditions model, the Resource-Based View of the firm (Barney, 1991), and Social Exchange Theory (Blau, 1964). Four hypotheses are evaluated through evidence synthesis. The results are clear: organizational culture is a powerful antecedent of employee engagement; AI adoption in HRM tends to strengthen engagement, but only when cultural conditions support it; AI mediates the culture-to-engagement pathway through what this paper calls three channels — enhanced meaningfulness, enhanced psychological safety, and enhanced resource availability; and cultural readiness for digital transformation amplifies the whole effect. The bibliometric data tell a compelling story of their own: publication activity in this domain grew at an annual rate of 29.86%, peaked in 2025, and has reached 99% saturation by 2026 — a Gaussian growth model fits with R²=0.961. India has emerged as the leading contributor nation, displacing the Western dominance that characterized earlier literature. The paper concludes with practical recommendations for HR leaders and clear directions for the next generation of empirical research.