  We calculate the thermal rate of real-photon production in the quark-gluon
plasma at a temperature of $T=254$ MeV using lattice QCD. The calculation is
based on the difference between the spatially transverse and longitudinal parts
of the polarization tensor, which has the advantage of falling off rapidly at
large frequencies. We obtain this linear combination in the time-momentum
representation from lattice QCD with two flavors of quarks in the continuum
limit with a precision of about two parts per mille. Applying a theoretically
motivated fit ansatz for the associated spectral function, we obtain values for
the photon rate that are in line with QCD weak-coupling calculations; for
photon momenta $ 1.0\leq k[{\rm GeV}]\leq 1.4$, our non-perturbative results
constrain the rate to be no larger than twice the weak-coupling prediction. We
also provide a physics interpretation of the electromagnetic spectral functions
valid for all frequencies and momenta.
