Accurate and efficient traffic flow prediction is crucial for modern urban transportation systems, directly impacting the effectiveness of intelligent traffic management and sustainable mobility solutions. Current spatio-temporal graph neural networks often fail to balance prediction accuracy and computational efficiency when modeling complex traffic patterns – a critical limitation for real-time applications requiring both precision and rapid processing. This paper presents UniTCP, a novel framework advancing urban traffic flow prediction through three key innovations: (1) The introduction of Universal Polynomial Basis (UniBasis) overcomes limitations of traditional spectral graph convolution by adaptively constructing optimal polynomial filters through data-driven learning, extending the concept of homophily ratio from node classification to multivariate time series forecasting and enabling dynamic modeling of complex spatial dependencies across heterogeneous traffic networks. (2) The innovative Temporal Convolutional Projection Module (TCPM) synergizes multi-scale convolutional branches with trend-aware pooling to comprehensively capture both transient traffic fluctuations and persistent periodic patterns, establishing a new paradigm for efficient temporal feature extraction. (3) A unified architecture integrating node-adaptive parameter learning with time-variant graph structure generation achieves optimal performance-efficiency balance through spectral domain parameterization and spatio-temporal embedding fusion. Experimental validation across four public datasets confirms the framework’s superior performance in addressing three core challenges: precise modeling of nonlinear spatio-temporal dependencies, computational resource optimization, and effective generalization across diverse traffic networks. The results demonstrate significant improvements in both prediction accuracy and operational efficiency compared to existing state-of-the-art approaches.