In this paper, we experimentally demonstrate a strong correlation between the frequencies of the Raman pump and the Raman probe inside an optically pumped Raman laser. We show that the correlation is due to rapid adjustment of the phase of the dipoles that produce the Raman gain, following a sudden jump in the phase of the Raman pump. A detailed numerical model validates this interpretation of the phase correlation. The width of the spectrum of the beat between the Raman pump and the Raman laser is significantly narrowed due to this correlation. As a result, the minimum measurable change in the cavity length, for a given linewidth of the Raman pump laser, is substantially reduced. Therefore, this finding is expected to enhance the sensitivity of such a laser in various metrological applications (e.g., accelerometry).