Vector-acoustic full-waveform inversion (VAFWI) directly inverts vector-acoustic (VA) data, which consist of pressure and particle displacement components, at the cost of conventional acoustic full-waveform inversion (FWI). VA data contain information about the direction of arrival of the recorded seismic waves. In VAFWI, this directional information is taken into account by introducing an appropriate data weighting. With this weighting, in the geometry of a marine seismic experiment, the VAFWI adjoint calculation approximates inverse wavefield extrapolation, resulting in the natural separation of up- and downgoing recorded waves. If the free-surface effects are modeled during the inversion, the wave separation leads to (1) suppression of surface-related artifacts, (2) constructive interference of receiver ghosts with their primaries leading to preservation of the low-frequency content in the adjoint fields, and (3) compensation for insufficient spatial wavefield sampling on the receiver side. The horizontal displacement component helps interpolate the missing data. Synthetic examples demonstrate that for undersampled data, VAFWI consistently recovers the subsurface properties with higher resolution and fewer artifacts than conventional FWI.