Using H I absorption spectra from the International Galactic Plane Survey, a new method is implemented to resolve the kinematic distance ambiguity for 75 H II regions with known systemic velocities from radio recombination lines. A further 40 kinematic distance determinations are made for H II region candidates without known systemic velocities through an investigation of the presence of H I absorption around the terminal velocity. New kinematic distance determinations can be used to further constrain spiral arm parameters and the location and extent of other structures in the Milky Way disk. H I absorption toward continuum sources beyond the solar circle is also investigated. Follow-up studies of H I at higher resolution than the 1' to 2' of existing Galactic Plane Surveys will provide kinematic distances to many more H II regions on the far side of the Galactic center. On the basis of the velocity channel summation technique developed in this paper, a much larger sample of H II regions will be analyzed in a future paper to remove the near-far distance ambiguity.