We examine the pairing process of supermassive black holes (SMBHs) down to scales of 20-100 pc using a set of N-body/SPH simulations of binary mergers of disk galaxies with mass ratios of 1:4 and 1:10. Our numerical experiments are designed to represent merger events occurring at various cosmic epochs. The initial conditions of the encounters are consistent with the ΛCDM paradigm of structure formation, and the simulations include the effects of radiative cooling, star formation (SF), and supernovae feedback. We find that the pairing of SMBHs depends sensitively on the amount of baryonic mass preserved in the center of the companion galaxies during the last phases of the merger. In particular, due to the combination of gasdynamics and SF, we find that a pair of SMBHs can form efficiently in 1:10 minor mergers, provided that galaxies are relatively gas-rich (gas fractions of 30% of the disk mass) and that the mergers occur at relatively high redshift (z ~ 3), when dynamical friction timescales are shorter. Since 1:10 mergers are most common events during the assembly of galaxies, and mergers are more frequent at high redshift when galaxies are also more gas-rich, our results have positive implications for future gravitational wave experiments such as the Laser Interferometer Space Antenna.