Recent progress in ML and LLMs has improved vulnerability detection, and recent datasets have reduced label noise and unrelated code changes. However, most existing approaches still operate at the function level, where models are asked to predict whether a single function is vulnerable without inter-procedural context. In practice, vulnerability presence and root cause often depend on contextual information. Naively appending such context is not a reliable solution: real-world context is long, redundant, and noisy, and we find that unstructured context frequently degrades the performance of strong fine-tuned code models. We present CPRVul, a context-aware vulnerability detection framework that couples Context Profiling and Selection with Structured Reasoning. CPRVul constructs a code property graph, and extracts candidate context. It then uses an LLM to generate security-focused profiles and assign relevance scores, selecting only high-impact contextual elements that fit within the model's context window. In the second phase, CPRVul integrates the target function, the selected context, and auxiliary vulnerability metadata to generate reasoning traces, which are used to fine-tune LLMs for reasoning-based vulnerability detection. We evaluate CPRVul on three high-quality vulnerability datasets: PrimeVul, TitanVul, and CleanVul. Across all datasets, CPRVul consistently outperforms function-only baselines, achieving accuracies ranging from 64.94% to 73.76%, compared to 56.65% to 63.68% for UniXcoder. Specifically, on the challenging PrimeVul benchmark, CPRVul achieves 67.78% accuracy, outperforming prior state-of-the-art approaches, improving accuracy from 55.17% to 67.78% (22.9% improvement). Our ablations further show that neither raw context nor processed context alone benefits strong code models; gains emerge only when processed context is paired with structured reasoning.