We present the first gas dynamical simulations of the photoevaporation of cosmological minihalos overtaken by the ionization fronts which swept through the IGM during reionization in a LCDM universe, including the effects of radiative transfer. We demonstrate the phenomenon of I-front trapping inside minihalos, in which the weak, R-type fronts which traveled supersonically across the IGM decelerated when they encountered the dense, neutral gas inside minihalos, becoming D-type I-fronts, preceded by shock waves. For a minihalo with virial temperature T_vir < 10^4 K, the I-front gradually burned its way through the minihalo which trapped it, removing all of its baryonic gas by causing a supersonic, evaporative wind to blow backwards into the IGM, away from the exposed layers of minihalo gas just behind the advancing I-front. Such hitherto neglected feedback effects were widespread during reionization. N-body simulations and analytical estimates of halo formation suggest that sub-kpc minihalos such as these, with T_vir < 10^4 K, were so common as to cover the sky around larger-mass source halos and possibly dominate the absorption of ionizing photons. This means that previous estimates of the number of ionizing photons per H atom required to complete reionization which neglected this effect may be too low. Regardless of their effect on the progress of reionization, however, the minihalos were so abundant that random lines of sight thru the high-z universe should encounter many of them, which suggests that it may be possible to observe the processes described here in the absorption spectra of distant sources.

34 pages, 34 figures, submitted to MNRAS. Computer animations at http://galileo.as.utexas.edu