We report the first measurements with sub-kiloparsec spatial resolution of strongly inverted gas-phase metallicity gradients in two dwarf galaxies at z ∼ 2. The galaxies have stellar masses ∼109 , specific star formation rate ∼20 Gyr-1, and global metallicity (1/4 solar), assuming the strong-line calibrations of [O iii]/Hβ and [O ii]/Hβ from Maiolino et al. Their radial metallicity gradients are measured to be highly inverted, i.e., 0.122 ± 0.008 and 0.111 ± 0.017 dex kpc-1, which is hitherto unseen at such small masses in similar redshift ranges. From the Hubble Space Telescope observations of the source nebular emission and stellar continuum, we present two-dimensional spatial maps of star formation rate surface density, stellar population age, and gas fraction, which show that our galaxies are currently undergoing rapid mass assembly via disk inside-out growth. More importantly, using a simple chemical evolution model, we find that the gas fractions for different metallicity regions cannot be explained by pure gas accretion. Our spatially resolved analysis based on a more advanced gas regulator model results in a spatial map of net gaseous outflows, triggered by active central starbursts, that potentially play a significant role in shaping the spatial distribution of metallicity by effectively transporting stellar nucleosynthesis yields outwards. The relation between wind mass loading factors and stellar surface densities measured in different regions of our galaxies shows that a single type of wind mechanism, driven by either energy or momentum conservation, cannot explain the entire galaxy. These sources present a unique constraint on the effects of gas flows on the early phase of disk growth from the perspective of spatially resolved chemical evolution within individual systems.