Multiway-or tensor-based decoding techniques for brain-computer interfaces (BCIs) are believed to better account for the multilinear structure of brain signals than conventional vector-or matrix-based ones. However, despite their outlook on significant performance gains, the used parameter optimization approach is often too computationally demanding so that conventional techniques are still preferred. We propose two novel tensor factorizations which we integrate into our block-term tensor regression (BTTR) algorithm and further introduce a marginalization procedure that guarantees robust predictions while reducing the risk of overfitting (generalized regression). BTTR accounts for the underlying (hidden) data structure in a fully automatic and computationally efficient manner, leading to a significant performance gain over conventional vector-or matrix-based techniques in a challenging real-world application. As a challenging real-world application, we apply BTTR to accurately predict single finger movement trajectories from intracranial recordings in human subjects. We compare the obtained performance with that of the state-of-the-art.