This paper examines the growing impact of Generative Artificial Intelligence (GenAI), including large language models and multimodal foundation models, on enterprise software quality assurance. While existing research has largely focused on isolated use cases such as test case generation or defect prediction, there remains a significant gap in understanding how GenAI can be systematically integrated across the full quality assurance lifecycle in high-volume, mission-critical enterprise systems. To address this gap, the paper proposes a comprehensive and practitioner-informed framework for the responsible adoption and governance of GenAI in enterprise quality engineering. The Generative AI Quality Assurance Governance Framework (GAQAGF) is introduced as a structured model consisting of four integrated layers: intelligent capability alignment, domain context injection, validation governance, and continuous assurance feedback. The study further identifies and formalizes seven categories of failure modes specific to enterprise transaction environments, including business rule hallucination, transaction state inconsistency, compliance misalignment, temporal context degradation, cross-service semantic drift, regulatory constraint bypass, and adversarial input blindness. These failure modes highlight the unique risks introduced by GenAI when applied to complex, distributed enterprise systems. Empirical observations from enterprise case studies across retail transaction platforms, financial systems, and telecommunications provisioning environments demonstrate measurable improvements when structured GenAI governance is applied. These include up to 47% improvement in test coverage, 63% reduction in manual test authoring effort, and 38% improvement in edge case defect detection, along with significant gains in AI-generated test quality. In addition, the paper introduces a maturity model for enterprise GenAI adoption, outlining a progression from experimental usage to fully governed, continuous assurance ecosystems. The work contributes to the broader fields of AI-assisted software engineering, enterprise systems, and digital transformation by providing both conceptual and practical foundations for integrating GenAI into mission-critical quality assurance workflows.