Using heavy quark effective field theory, exponentiation of Sudakov double logarithms, and perturbative factorization theorems for exclusive processes, we calculate the amplitude for the semileptonic decay of mesons with a single, very heavy quark into \ensuremath{\pi} and \ensuremath{\rho} for a large hadronic recoil momentum. A formula for these large-recoil widths is obtained in terms of two-particle wave functions of the heavy and light mesons and applied to semileptonic decays of the B.