HSI-SR aims to enhance spatial resolution while preserving spectrally faithful and physically plausible characteristics. Recent methods have achieved great progress by leveraging spatial correlations to enhance spatial resolution. However, these methods often neglect spectral consistency across bands, leading to spurious oscillations and physically implausible artifacts. While spectral consistency can be addressed by designing the network architecture, it results in a loss of generality and flexibility. To address this issue, we propose a lightweight plug-and-play rectifier, physically priors Spectral Rectification Super-Resolution Network (SR$^{2}$-Net), which can be attached to a wide range of HSI-SR models without modifying their architectures. SR$^{2}$-Net follows an enhance-then-rectify pipeline consisting of (i) Hierarchical Spectral-Spatial Synergy Attention (H-S$^{3}$A) to reinforce cross-band interactions and (ii) Manifold Consistency Rectification (MCR) to constrain the reconstructed spectra to a compact, physically plausible spectral manifold. In addition, we introduce a degradation-consistency loss to enforce data fidelity by encouraging the degraded SR output to match the observed low resolution input. Extensive experiments on multiple benchmarks and diverse backbones demonstrate consistent improvements in spectral fidelity and overall reconstruction quality with negligible computational overhead. Our code will be released upon publication.