We report the results of a study of the exclusive charmless semileptonic decay, B0→π-ℓ+ν, undertaken with approximately 227×106 BB̄ pairs collected at the Υ(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with an innovative loose neutrino reconstruction technique. We obtain partial branching fractions in 12 bins of q2, the momentum transfer squared, from which we extract the f+(q2) form-factor shape and the total branching fraction B(B0→π-ℓ+ν)=(1.46±0.07stat±0.08syst)×10-4. Based on a recent unquenched lattice QCD calculation of the form factor in the range q2>16GeV2, we find the magnitude of the Cabibbo-Kobayashi-Maskawa matrix element |Vub| to be (4.1±0.2stat±0.2syst+0.6-0.4FF) ×10-3, where the last uncertainty is due to the normalization of the form factor. © 2007 The American Physical Society.