As AI agents transition from research prototypes to enterprise production systems, the tool interfaces they consume remain rooted in human-oriented CRUD paradigms. This paper identifies five fundamental architectural mismatches between conventional APIs and autonomous agent requirements: exact-identifier dependence, rendering-oriented responses, single-shot interaction assumptions, user-equivalent authorization, and opaque error semantics. We propose the Agent-First Tool API paradigm, comprising three integrated mechanisms: (1) a Six-Verb Semantic Protocol that decomposes tool interactions into search, resolve, preview, execute, verify, and recover phases; (2) a Normalized Tool Contract (NTC) providing structured decision-support metadata including confidence scores, evidence chains, and suggested next actions; and (3) a dual-layer governance pipeline combining static capability policies with dynamic risk escalation. The paradigm is implemented and validated in a production multi-tenant SaaS platform serving 85 registered tools across 6 business domains. Comparative experiments on 50 real operational tasks demonstrate that Agent-First APIs achieve 88% end-to-end task success rate versus 64% for optimized CRUD baselines (+37.5%), while reducing required human interventions by 72.7% and improving autonomous error recovery by 5.8x. We establish that the paradigm is orthogonal and complementary to transport-layer standards such as MCP, operating as the semantic application layer above existing tool discovery and invocation protocols.