.The photon emission rate of a thermally equilibrated system is determined by the imaginary part of the in-medium retarded correlator of the electromagnetic current transverse to the spatial momentum of the photon. In a Lorentz-covariant theory, this correlator can be parametrized by a scalar function mathcal{G}_R(ucdot mathcal{K},mathcal{K}^{2}), where u is the fluid four-velocity and mathcal{K} corresponds to the momentum of the photon. We propose to compute the analytic continuation of mathcal{G}_R(ucdot mathcal{K},mathcal{K}^{2}) at fixed, vanishing virtuality mathcal{K}^{2}, to imaginary values of the first argument, ucdot mathcal{K} = iomega_{n}. At these kinematics, the retarded correlator is equal to the Euclidean correlator G_{E}(omega_{n},k=iomega_{n}), whose first argument is the Matsubara frequency and the second is the spatial momentum. The Euclidean correlator, which is directly accessible in lattice QCD simulations, must be given an imaginary spatial momentum in order to realize the photon on-shell condition. Via a once-subtracted dispersion relation that we derive in a standard way at fixed mathcal{K}^{2}=0, the Euclidean correlator with imaginary spatial momentum is related to the photon emission rate. The relation allows for a more direct probing of the real-photon emission rate of the quark-gluon plasma in lattice QCD than the dispersion relations which have been used so far, the latter being at fixed spatial photon momentum k and thus involving all possible virtualities of the photon.