Open-source software projects are foundational to modern software ecosystems, with the Linux kernel standing out as a critical exemplar due to its ubiquity and complexity. Although security patches are continuously integrated into the Linux mainline kernel, downstream maintainers often delay their adoption, creating windows of vulnerability. A key reason for this lag is the difficulty in identifying security-critical patches, particularly those addressing exploitable vulnerabilities such as out-of-bounds (OOB) accesses and use-after-free (UAF) bugs. This challenge is exacerbated by intentionally silent bug fixes, incomplete or missing CVE assignments, delays in CVE issuance, and recent changes to the CVE assignment criteria for the Linux kernel. While fine-grained patch classification approaches exist, they exhibit limitations in both coverage and accuracy. In this work, we identify previously unexplored opportunities to significantly improve fine-grained patch classification. Specifically, by leveraging cues from commit titles/messages and diffs alongside appropriate code context, we develop DUALLM, a dual-method pipeline that integrates two approaches based on a Large Language Model (LLM) and a fine-tuned small language model. DUALLM achieves 87.4% accuracy and an F1-score of 0.875, significantly outperforming prior solutions. Notably, DUALLM successfully identified 111 of 5,140 recent Linux kernel patches as addressing OOB or UAF vulnerabilities, with 90 true positives confirmed by manual verification (many do not have clear indications in patch descriptions). Moreover, we constructed proof-of-concepts for two identified bugs (one UAF and one OOB), including one developed to conduct a previously unknown control-flow hijack as further evidence of the correctness of the classification.