We report a facile method of ordering block copolymer (BCP) morphologies in which the conventional two-step casting and annealing steps are replaced by a single-step process where microphase separation and grain coarsening are seamlessly integrated within the casting protocol. This is achieved by slowing down solvent evaporation during casting by introducing a nonvolatile solvent into the BCP casting solution that effectively prolongs the duration of the grain-growth phase. We demonstrate the utility of this solvent evaporation annealing (SEA) method by producing well-ordered large-molecular-weight BCP thin films in a total processing time shorter than 3 min without resorting to any extra laboratory equipment other than a basic casting device, i.e., spin- or blade-coater. By analyzing the morphologies of the quenched samples, we identify a relatively narrow range of polymer concentration in the wet film, just above the order-disorder concentration, to be critical for obtaining large-grained morphologies. This finding is corroborated by the analysis of the grain-growth kinetics of horizontally oriented cylindrical domains where relatively large growth exponents (1/2) are observed, indicative of a more rapid defect-annihilation mechanism in the concentrated BCP solution than in thermally annealed BCP melts. Furthermore, the analysis of temperature-resolved kinetics data allows us to calculate the Arrhenius activation energy of the grain coarsening in this one-step BCP ordering process.