Current embodiments of photoacoustic imaging require either serial detection with a single-element ultrasonic transducer or parallel detection with an ultrasonic array, necessitating a trade-off between cost and throughput. Here, we present photoacoustic topography through an ergodic relay (PATER) for low-cost high-throughput snapshot widefield imaging. Encoding spatial information with randomized temporal signatures through ergodicity, PATER requires only a single-element ultrasonic transducer to capture a widefield image with a single laser shot. We applied PATER to demonstrate both functional imaging of hemodynamic responses and high-speed imaging of blood pulse wave propagation in mice in vivo. Leveraging the high frame rate of 2 kHz, PATER tracked and localized moving melanoma tumor cells in the mouse brain in vivo, which enabled flow velocity quantification and super-resolution imaging. Among the potential biomedical applications of PATER, wearable monitoring of human vital signs in particular is envisaged.