Single-photon lidar (SPL) is a promising technology for depth measurement at long range or from weak reflectors because of the sensitivity to extremely low light levels. However, constraints on the timing resolution of existing arrays of single-photon avalanche diode (SPAD) detectors limit the precision of resulting depth estimates. In this work, we describe an implementation of subtractively-dithered SPL that can recover high-resolution depth estimates despite the coarse resolution of the detector. Subtractively-dithered measurement is achieved by adding programmable delays into the photon timing circuitry that introduce relative time shifts between the illumination and detection that are shorter than the time bin duration. Careful modeling of the temporal instrument response function leads to an estimator that outperforms the sample mean and results in depth estimates with up to 13 times lower root mean-squared error than if dither were not used. The simple implementation and estimation suggest that globally dithered SPAD arrays could be used for high spatial- and temporal-resolution depth sensing.