An analysis of B to pi0 l nu and B to eta l nu decays using the neutrino reconstruction technique is presented. The dataset consists of 535 million BB pairs in 492 fb^−1 of data collected with the Belle detector at the KEKB asymmetric e+e− collider. The measured B to pi0 l nu and B to eta l nu branching fractions are B(B to pi0 l nu) = (0.68 ± 0.09 ± 0.11 ± 0.04)×10^−4 and B(B to eta l nu) = (0.42 ± 0.13)×10^−4. The errors on the pi0 measurement are statistical, experimental systematic, and due to b to u l nu modelling, respectively; that on the eta is statistical only. The B to pi0 l nu branching fraction is measured in three q^2 bins: q^2 < 8 GeV^2, 8 GeV^2 ≤ q^2 < 16 GeV^2, and 16 GeV^2 ≤ q^2. The Cabibbo-Kobayashi-Maskawa quark-mixing matrix element |Vub| is extracted from the B to pi0 l nu branching fraction using a Light-Cone Sum Rules form factor extrapolated to the full q^2 range, and is found to be |Vub| = (3.29 ± 0.23 ± 0.27 ± 0.05)×10^−3, where the errors are statistical, experimental systematic, and theoretical, respectively.