Artificial intelligence systems are increasingly embedded in high-stakes decision environments, yet many governance approaches focus primarily on policy guidance rather than operational stability mechanisms. As AI deployments scale, organizations require governance architectures capable of maintaining reliable, auditable, and accountable behavior over time. This paper introduces the AI Governance Control Stack for Operational Stability, a layered governance architecture designed to ensure traceable and resilient AI system behavior. The proposed control stack integrates six complementary governance layers: system-of-record version governance, evidence-based verification, decision-time explainability logging, telemetry monitoring, model drift detection, and governance escalation. Together, these layers provide a structured mechanism for preserving governance integrity across the AI lifecycle while enabling organizations to detect instability, respond to emerging risks, and maintain regulatory accountability. The architecture aligns operational governance practices with emerging regulatory and standards frameworks, including the EU AI Act, ISO/IEC 42001 Artificial Intelligence Management Systems, and the NIST AI Risk Management Framework. By combining explainability infrastructure with continuous monitoring and human oversight mechanisms, the governance control stack provides a practical blueprint for achieving hardened AI governance in complex enterprise environments. The paper contributes a conceptual governance architecture and a framework alignment analysis demonstrating how operational stability mechanisms can strengthen responsible AI implementation. The findings suggest that organizations must move beyond static policy frameworks toward integrated governance control systems capable of sustaining trustworthy AI operation in dynamic environments.