Decoding brain activity from non-invasive electroencephalography (EEG) is crucial for brain-computer interfaces (BCIs) and the study of brain disorders. Notably, end-to-end EEG decoding has gained widespread popularity in recent years owing to the remarkable advances in deep learning research. However, many EEG studies suffer from limited sample sizes, making it difficult for existing deep learning models to effectively generalize to highly noisy EEG data. To address this fundamental limitation, this paper proposes a novel end-to-end EEG decoding algorithm that utilizes a low-rank weight matrix to encode both spatio-temporal filters and the classifier, all optimized under a principled sparse Bayesian learning (SBL) framework. Importantly, this SBL framework also enables us to learn hyperparameters that optimally penalize the model in a Bayesian fashion. The proposed decoding algorithm is systematically benchmarked on five motor imagery BCI EEG datasets ( N=192) and an emotion recognition EEG dataset ( N=45), in comparison with several contemporary algorithms, including end-to-end deep-learning-based EEG decoding algorithms. The classification results demonstrate that our algorithm significantly outperforms the competing algorithms while yielding neurophysiologically meaningful spatio-temporal patterns. Our algorithm therefore advances the state-of-the-art by providing a novel EEG-tailored machine learning tool for decoding brain activity.