We propose and apply a new test of Einsteins equivalence principle (EEP) based on the gravitational redshift induced by the central supermassive black hole of quasars in the surrounding accretion disk. Specifically, we compare the observed gravitational redshift of the Fe III 2039-2113 emission line blend in quasars with the predicted values in a wide, uncharted, cosmic territory (0 zcosm 3). For the first time we measure, with statistical uncertainties comparable or better than those of other classical methods outside the solar system, the ratio between the observed gravitational redshifts and the theoretical predictions in 10 independent cosmological redshift bins in the 1 zcosm 3 range. The average of the measured over predicted gravitational redshifts ratio in this cosmological redshift interval is $\langle {z}_{g}^{m}/{z}_{g}^{p}\rangle =1.05\pm 0.06$ with scatter 0.13 0.05 showing no cosmological evolution of EEP within these limits. This method can benefit from larger samples of measurements with better signal-to-noise ratios, paving the way for high-precision tests (below 1) of EEP on cosmological scales.