We present the Kepler photometric light-variation analysis of the late-type double-lined binary system V568 Lyr that is in the field of the high metallicity old open cluster NGC 6791. The radial velocity and the high-quality short-cadence light curve of the system are analysed simultaneously. The masses, radii and luminosities of the component stars are M-1 = 1.0886 +/- 0.0031 M-circle dot, M-2 = 0.8292 +/- 0.0026 M-circle dot, R-1 = 1.4203 +/- 0.0058 R-circle dot, R-2 = 0.7997 +/- 0.0015 R-circle dot, L-1 = 1.85 +/- 0.15 L-circle dot, L-2 = 0.292 +/- 0.018 L-circle dot and their separation is a = 31.060 +/- 0.025 R-circle dot. The distance to NGC 6791 is determined to be 4.260 +/- 0.290 kpc by analysis of this binary system. We fit the components of this well-detached binary system with evolution models made with the Cambridge STARS and EV(TWIN) codes to test low-mass binary star evolution. We find a good fit with a metallicity of Z = 0.04 and an age of 7.704 Gyr. The standard tidal dissipation, included in EV(TWIN) is insufficient to arrive at the observed circular orbit unless it formed rather circular to begin with.