The massive stars in the Galactic center inner arcsecond share analogous properties with the so-called Hot Jupiters. Most of these young stars have highly eccentric orbits and were probably not formed in situ. It has been proposed that these stars acquired their current orbits from the tidal disruption of compact massive binaries scattered toward the proximity of the central supermassive black hole. Assuming a binary star formed in a thin gaseous disk beyond 0.1 pc from the central object, we investigate the relevance of disk-satellite interactions to harden the binding energy of the binary, and to drive its inward migration. A massive, equal-mass binary star is found to become more tightly wound as it migrates inward toward the central black hole. The migration timescale is very similar to that of a single-star satellite of the same mass. The binary's hardening is caused by the formation of spiral tails lagging the stars inside the binary's Hill radius. We show that the hardening timescale is mostly determined by the mass of gas inside the binary's Hill radius and that it is much shorter than the migration timescale. We discuss some implications of the binary's hardening process. When the more massive (primary) components of close binaries eject most their mass through supernova explosion, their secondary stars may attain a range of eccentricities and inclinations. Such processes may provide an alternative unified scenario for the origin of the kinematic properties of the central cluster and S-stars in the Galactic center as well as the high-velocity stars in the Galactic halo.