We report in this study how ocean-bottom seismometers (OBS) can be used as passive sonars to automatically detect, localize, and track moving acoustic sources at the ocean surface. We developed single-station methods based on direction of arrival and on multi-path interference measurements capable of handling continuous erratic signals emitted by ships. Based on a Bayesian mathematical framework, we developed an azimuthal detector and a radial detector and combined them into a fully automatic tracker. We tested the developed algorithm on seismic and hydroacoustic data recorded in the Indian Ocean by an OBS deployed at 4300 m depth, 200 km west of La Réunion Island. We quantified the performances using archives of commercial-vessel trajectories in the area provided by the Automatic Identification System. Detectors demonstrate capabilities in the detection range up to 100 km from the OBS with azimuthal accuracies of a few degrees and with distance accuracies of a few hundred of meters. We expect the method to be easily transposed to any other kind of sources (such as marine mammals).