We show that the light curve of the double GeV+optical flash in GRB 130427A is consistent with radiation from the blast wave in a wind-type medium with density parameter $A=rho r^2sim 5times 10^{10}$ g cm$^{-1}$. The peak of the flash is emitted by copious $e^pm$ pairs created and heated in the blast wave; our first-principle calculation determines the pair-loading factor and temperature of the shocked plasma. Using detailed radiative transfer simulations we reconstruct the observed double flash. The optical flash is dominated by synchrotron emission from the thermal plasma behind the forward shock, and the GeV flash is produced via inverse Compton (IC) scattering by the same plasma. The seed photons for IC scattering are dominated by the prompt MeV radiation during the first tens of seconds, and by the optical to X-ray afterglow thereafter. IC cooling of the thermal plasma behind the forward shock reproduces all GeV data from a few seconds to $sim 1$ day. We find that the blast wave Lorentz factor at the peak of the flash is $Gammaapprox 200$, and the forward shock magnetization is $epsilon_Bsim 2times 10^{-4}$. An additional source is required by the data in the optical and X-ray bands at times $>10^2$ s; we speculate that this additional source may be a long-lived reverse shock in the explosion ejecta.
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