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Class-incremental learning (CIL) with pre-trained models (PTMs) faces a critical trade-off between efficient adaptation and long-term stability. While analytic learning enables rapid, recursive closed-form updates, its efficacy is often compromised by accumulated errors and feature incompatibility. In this paper, we first conduct a systematic study to dissect the failure modes of PTM-based analytic CIL, identifying representation rigidity as the primary bottleneck. Motivated by these insights, we propose \textbf{VILA}, a novel dual-branch framework that advances analytic CIL via a two-level vision-language calibration strategy. Specifically, we coherently fuse plastic, task-adapted features with a frozen, universal semantic anchor at the feature level through geometric calibration, and leverage cross-modal priors at the decision level to rectify prediction bias. This confluence maintains analytic-learning's extreme efficiency while overcoming its inherent brittleness. Extensive experiments across eight benchmarks demonstrate that VILA consistently yields superior performance, particularly in fine-grained and long-sequence scenarios. Our framework harmonizes high-fidelity prediction with the simplicity of analytic learning. Our code is available at this https URL