Expertise in vertical domains requires more than exposing LLMs to vast corpora; it demands the systematic learning of complex logic. Standard fine-tuning often treats data as an unstructured collection, failing to capture the dependencies needed for high-level reasoning. We propose Domain Knowledge Annealing (DKA), a curriculum learning paradigm designed to improve domain proficiency. Inspired by physical annealing, DKA organizes training from local to global: it starts by injecting discrete concepts via entity-centric samples and progressively advances to synthesizing complex, inter-document relationships. This progression allows the model to integrate isolated facts into a coherent knowledge system. Experiments on Linguistics and Law benchmarks show that DKA outperforms standard strategies, achieving state-of-the-art results among comparably sized models in domain-specific reasoning.