The precise determination of the CKM matrix element |Vub| is crucial in testing the Standard Model mechanism for CP violation. From a sample of 88 million BB pairs collected with the MBAR detector, charmless semileptonic B decays are selected using simultaneous requirements on the electron energy, Ee, and the invariant mass squared of the electron-neutrino pair, q2. The partial branching fraction, unfolded for detector effects, is determined in a region of the q2-Ee plane where the dominating semileptonic decays to charm mesons are highly suppressed. Theoretical calculations based on the Heavy Quark Expansion allows for a determination of |Vub| = (3.95 ± 0.27 +0.58 -0:42 ± 0.25) x 10 3, where the errors represent experimental, heavy quark parameters and theoretical uncertainties, respectively.