The gravitational redshift induced by stellar surface gravity is notoriously difficult to measure for non-degenerate stars, since its amplitude is small in comparison with the typical Doppler shift induced by stellar radial velocity. In this study, we make use of the large observational data set of the Gaia mission to achieve a significant reduction of noise caused by these random stellar motions. By measuring the differences in velocities between the components of the pairs of comoving stars and wide binaries, we are able to statistically measure the combined effects of gravitational redshift and convective blueshifting of spectral lines, and nullify the effect of the peculiar motions of the stars. For the subset of stars considered in this study, we find a positive correlation between the observed differences in Gaia radial velocities and the differences in surface gravity and convective blueshift inferred from effective temperature and luminosity measurements. The results rule out a null signal at the 5{sigma} level for our full data set. Additionally, we study the subdominant effects of binary motion, and possible systematic errors in radial velocity measurements within Gaia. Results from the technique presented in this study are expected to improve significantly with data from the next Gaia data release. Such improvements could be used to constrain the mass-luminosity relation and stellar models that predict the magnitude of convective blueshift.