Image quality of positron emission tomography (PET) reconstructions is degraded by subject motion occurring during the acquisition. Magnetic resonance (MR)-based motion correction approaches have been studied for PET/MR scanners and have been successful at capturing regular motion patterns, when used in conjunction with surrogate signals (e.g. navigators) to detect motion. However, handling irregular respiratory motion and bulk motion remains challenging. In this work, we propose an MR-based motion correction method relying on subspace-based real-time MR imaging to estimate motion fields used to correct PET reconstructions. We take advantage of the low-rank characteristics of dynamic MR images to reconstruct high-resolution MR images at high frame rates from highly undersampled k-space data. Reconstructed dynamic MR images are used to determine motion phases for PET reconstruction and estimate phase-to-phase nonrigid motion fields able to capture complex motion patterns such as irregular respiratory and bulk motion. MR-derived binning and motion fields are used for PET reconstruction to generate motion-corrected PET images. The proposed method was evaluated on in vivo data with irregular motion patterns. MR reconstructions accurately captured motion, outperforming state-of-the-art dynamic MR reconstruction techniques. Evaluation of PET reconstructions demonstrated the benefits of the proposed method in terms of motion artifacts reduction, improving the contrast-to-noise ratio by up to a factor 3 and achieveing a target-to-background ratio up to 90% superior compared to standard/uncorrected methods. The proposed method can improve the image quality of motion-corrected PET reconstructions in clinical applications.