We numerically study the behavior of a collection of overdamped Brownian particles in a channel, in the presence of a flow field applied on similar but slower particles in a wide chamber in contact with the channel. For a suitable range of shear rates, we find that the flow field induces a unidirectional drift in the confined particles, and is stronger for narrower channels. The average drift velocity initially rises with increasing shear rate, then shows saturation for a while, thereafter starts decreasing, in qualitative agreement with recent theoretical studies [Phys. Rev. B 70, 205423 (2004)] based on Brownian drag and ``loss of grip.″ Interestingly, if the sign of the interspecies interaction is reversed, the direction of the induced drift remains the same, but the flow rate at which loss of grip occurs is lower, and the level of fluctuations is higher.