We present a lattice QCD calculation of B→πlν semileptonic decay form factors in the small pion recoil momentum region. The calculation is performed on a quenched 163×48 lattice at β=5.9 with the nonrelativistic QCD action including the full 1/M terms. The form factors f1(v⋅kπ) and f2(v⋅kπ) defined in the heavy quark effective theory for which the heavy quark scaling is manifest are adopted, and we find that the 1/M correction to the scaling is small for the B meson. The dependence of the form factors on the light quark mass and on the recoil energy is found to be mild, and we use a global fit of the form factors at various quark masses and recoil energies to obtain model independent results for the physical differential decay rate. We find that the B* pole contribution dominates the form factor f+(q2) for small pion recoil energy, and obtain the differential decay rate integrated over the kinematic region q2>18 GeV2 to be |Vub|2×(1.18±0.37±0.08±0.31) psec-1, where the first error is statistical, the second is that from perturbative calculation, and the third is the systematic error from the finite lattice spacing and the chiral extrapolation. We also discuss the systematic errors in the soft pion limit for f0(qmax2) in the present simulation.