We examine the coincidence of times of high y-ray flux and ejections of superluminal components from the core in EGRET blazars based on a Very Long Baseline Array (VLBA) monitoring program at 22 and 43 GHz from 1993 November to 1997 July. In 23 cases of γ-ray flares for which sufficient VLBA data exist, 10 of the flares (in eight objects) fall within 1 σ uncertainties of the extrapolated epoch of zero separation from the core of a superluminal radio component. In each of two sources (0528 + 134 and 1730-130), two successive γ-ray flares were followed by the appearance of new superluminal components. We carried out statistical simulations that show that if the number of coincidences is ≥ 10, the radio and γ-ray events are associated with each other at greater than 99.999% confidence. Our analysis of the observed behavior, including variability of the polarized radio flux, of the sources before, during, and after the γ-ray flares suggests that the γ-ray events occur in the superluminal radio knots. This implies that the γ-ray flares are caused by inverse Compton scattering by relativistic electrons in the parsec-scale regions of the jet rather than closer to the central engine.