The early Universe hosted a large population of small dark matter `minihalos that were too small to cool and form stars on their own. These existed as static objects around larger galaxies until acted upon by some outside influence. Outflows, which have been observed around a variety of galaxies, can provide this influence in such a way as to collapse, rather than disperse the minihalo gas. Gray & Scannapieco performed an investigation in which idealized spherically-symmetric minihalos were struck by enriched outflows. Here we perform high-resolution cosmological simulations that form realistic minihalos, which we then extract to perform a large suite of simulations of outflow-minihalo interactions including non-equilibrium chemical reactions. In all models, the shocked minihalo forms molecules through non-equilibrium reactions, and then cools to form dense chemically homogenous clumps of star-forming gas. The formation of these high-redshift clusters will be observable with the next generation of telescopes, and the largest of them should survive to the present day, having properties similar to halo globular clusters.