We reconsider and update the QCD light-cone sum rules for $B\to π$ form factors. The gluon radiative corrections to the twist-2 and twist-3 terms in the correlation functions are calculated. The $\barMS$ $b$-quark mass is employed, instead of the one-loop pole mass used in the previous analyses. The light-cone sum rule for $f^+_Bπ(q^2)$ is fitted to the measured $q^2$-distribution in $B\to π l ν_l$, fixing the input parameters with the largest uncertainty: the Gegenbauer moments of the pion distribution amplitude. For the $B\to π$ vector form factor at zero momentum transfer we predict $f^+_Bπ(0)= 0.26^+0.04_-0.03$. Combining it with the value of the product $|V_ubf^+_Bπ(0)|$ extracted from experiment, we obtain $|V_ub|=(3.5± 0.4± 0.2± 0.1) × 10^-3$. In addition, the scalar and penguin $B\to π$ form factors $f^0_Bπ(q^2)$ and $f^T_Bπ(q^2)$ are calculated.