Legal Article Prediction (LAP) is a critical task in legal text classification, leveraging natural language processing (NLP) techniques to automatically predict relevant legal articles based on the fact descriptions of cases. As a foundational step in legal decision-making, LAP plays a pivotal role in determining subsequent judgments, such as charges and penalties. Despite its importance, existing methods face significant challenges in addressing the complexities of LAP. Supervised classification models (SCMs), such as CNN and BERT, struggle to fully capture intricate fact patterns due to their inherent limitations. Conversely, large language models (LLMs), while excelling in generative tasks, perform suboptimally in predictive scenarios due to the abstract and ID-based nature of legal articles. Furthermore, the diversity of legal systems across jurisdictions exacerbates the issue, as most approaches are tailored to specific countries and lack broader applicability. To address these limitations, we propose Uni-LAP, a universal framework for legal article prediction that integrates the strengths of SCMs and LLMs through tight collaboration. Specifically, in Uni-LAP, the SCM is enhanced with a novel Top-K loss function to generate accurate candidate articles, while the LLM employs syllogism-inspired reasoning to refine the final predictions. We evaluated Uni-LAP on datasets from multiple jurisdictions, and empirical results demonstrate that our approach consistently outperforms existing baselines, showcasing its effectiveness and generalizability.