Hyperspectral single image super-resolution (SISR) is a challenging task due to the difficulty of restoring fine spatial details while preserving spectral fidelity across a wide range of wavelengths, which limits the performance of conventional deep learning models. To address this challenge, we introduce Spectral-Spatial Unmixing Fusion (SSUF), a novel module that can be seamlessly integrated into standard 2D convolutional architectures to enhance both spatial resolution and spectral integrity. The SSUF combines spectral unmixing with spectral--spatial feature extraction and guides a ResNet-based convolutional neural network for improved reconstruction. In addition, we propose a custom Spatial-Spectral Gradient Loss function that integrates mean squared error with spatial and spectral gradient components, encouraging accurate reconstruction of both spatial and spectral features. Experiments on three public remote sensing hyperspectral datasets demonstrate that the proposed hybrid deep learning model achieves competitive performance while reducing model complexity.