We employ extensive computer simulations to study the flow behavior of spherical, nanoscale colloids in a viscoelastic solvent under Poiseuille flow. The systems are confined in a slit-like microfluidic channel, and viscoelasticity is introduced explicitly through the inclusion of polymer chains on the same length scale as the dispersed solute particles. We systematically study the effects of flow strength and polymer concentration, and identify a regime in which the colloids migrate to the centerline of the microchannel, expelling the polymer chains to the sides. This behavior was recently identified in experiments, but a detailed understanding of the underlying physics was lacking. To this end, we provide a detailed analysis of this phenomenon and discuss ways to maximize its effectiveness. The focusing mechanism can be exploited to separate and capture particles at the sub-micrometer scale using simple microfluidic devices, which is a crucial task for many biomedical applications, such as cell counting and genomic mapping.