Hyperspectral single-image super-resolution (SISR) remains a challenging task due to the difficulty of restoring fine spatial details and preserving spectral fidelity across a wide range of wavelengths, which inherently limits the performance of conventional deep learning models. To effectively address this challenge, we introduce a novel module called spectral–spatial unmixing fusion (SSUF), which can be seamlessly integrated into existing 2-D convolutional architectures to enhance both spatial resolution and spectral integrity. Specifically, the SSUF combines spectral unmixing and spectral–spatial feature extraction to subsequently guide a ResNet-based convolutional neural network (CNN). In addition, we employ a custom spatial–spectral gradient loss function, which integrates mean squared error (mse) with spatial and spectral gradient components, encouraging the model to accurately reconstruct features across both spatial and spectral dimensions. Experiments on three public remote sensing hyperspectral datasets demonstrate that our proposed hybrid deep learning (HDL) achieves competitive performance while reducing model complexity. The source codes are publicly available at: https://github.com/Usman1021/hsi-super-resolution