Using the east-west drift of equatorial spread-F (ESF) irregularities as tracers for horizontal bulk plasma motion, we show that a velocity shear (with altitude) in east-west plasma drift exists in the nighttime equatorial F-layer. When combined with incoherent-scatter measurements of the vertical motion of the F-layer, we find evidence that the two-dimensional plsama flow pattern in the F-region around E-region sunset resembles a vortex. The velocity vortex is attributed to (1) a velocity shear that is set up by the F-region dynamo that begins to function around E-region sunset, and (2) the postsunset rise of the F-layer. The existence of a velocity shear verifies the importance of the eastward neutral wind and F-region dynamo in nighttime equatorial plasma electrodynamics, and allows new interpretation for ESF generation processes.