We investigate the molecular evolution and D/H abundance ratios that develop as star formation proceeds from a dense molecular cloud core to a protostellar core, by solving a gas-grain reaction network applied to a one-dimensional radiative hydrodynamic model with infalling fluid parcels. Spatial distributions of gas and ice-mantle species are calculated at the first-core stage, and at times after the birth of a protostar. Gas-phase methanol and methane are more abundant than CO at radii r <~ 100 AU in the first-core stage, but gradually decrease with time, while abundances of larger organic species increase. The warm-up phase, when complex organic molecules are efficiently formed, is longer-lived for those fluid parcels infalling at later stages. The formation of unsaturated carbon chains (warm carbon-chain chemistry) is also more effective in later stages; C+, which reacts with CH4 to form carbon chains, increases in abundance as the envelope density decreases. The large organic molecules and carbon chains are strongly deuterated, mainly due to high D/H ratios in the parent molecules, determined in the cold phase. We also extend our model to simulate simply the chemistry in circumstellar disks, by suspending the one-dimensional infall of a fluid parcel at constant disk radii. The species CH3OCH3 and HCOOCH3 increase in abundance in 104-105 yr at the fixed warm temperature; both also have high D/H ratios.