Brillouin spectroscopy is a powerful tool for measuring the mechanical properties of materials without contact. The sensitivity to mechanical changes that a Brillouin spectrometer can detect is determined by the precision to which a spectral peak can be localized. The localization precision is however fundamentally limited by the low number of photons within a Brillouin measurement, as well as by intrinsic noise of the setup. Here, we present a method to improve the spectral sensitivity of Brillouin measurements by exploiting the autocorrelation function of the spectrum. We show that by performing a localization process on the autocorrelation function nearly 20% increase in localization precision can be obtained. This result is consistent between our theoretical treatment, numerical simulation and experimental results. We further study the effect of background noise on the precision improvement for realistic scenarios.