Compressed sensing is a powerful rapid imaging approach for Magnetic Resonance Imaging (MRI) and has been applied to many clinical applications. In this work, we propose a new use of sparsity in addition to speed. In particular, we present a novel way of handling respiratory motion using compressed sensing for dynamic contrast-enhanced MRI. The proposed technique, called XD-GRASP (eXtra-Dimensional Golden-angle RAdial Sparse Parallel MRI), sorts the continuously acquired radial k-space data into undersampled contrast phases at multiple respiratory motion states using the self-navigation properties of radial imaging and employs a multidimensional compressed sensing reconstruction to exploit sparsity along both contrast-enhancement and respiratory motion dimensions. XD-GRASP improves image quality and also enables to track respiratory motion during contrast enhancement, which can potentially be of clinical value.