We calculate the thermal rate of real-photon production in the quark-gluon plasma at a temperature of <math><mi>T</mi><mo>=</mo><mn>254</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math> 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. A representative result is <math><mi>d</mi><mi>Γ</mi><mo>(</mo><mi>k</mi><mo>)</mo><mo>/</mo><mi>d</mi><mi>k</mi><mo>=</mo><mo>(</mo><mn>1.</mn><msubsup><mn>5</mn><mrow><mo>−</mo><mn>1.5</mn></mrow><mrow><mo>+</mo><mn>2.1</mn></mrow></msubsup><mo>)</mo><mo>·</mo><mo>(</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi><msup><mo>)</mo><mrow><mo>−</mo><mn>4</mn></mrow></msup><mo>·</mo><mo>(</mo><mn>0.2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><msup><mo>)</mo><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> at <math><mi>k</mi><mo>=</mo><mn>1.2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> for the differential rate of photon production per unit volume of plasma.