For coupled linear cavity-random fiber Raman lasers, for the first time, to the best of our knowledge, we demonstrate a new mechanism of emergence of the random pulses, with the anomalous statistics satisfying optical rogue waves' criteria experimentally. The rogue waves appear as a result of the coupling of two Raman cascades, namely, a linear cavity laser with a wavelength of 1.55 µm and a random laser with a wavelength nearly 1.67 µm, along with coupling of the orthogonal states of polarization (SOPs). The coherent coupling of SOPs causes localization of the trajectories in the vicinity of these states, whereas polarization instability drives escape taking the form of chaotic oscillations. Antiphase dynamics in two cascades result in the suppression of low amplitude chaotic oscillations and enable the anomalous spikes, satisfying rogue waves criteria.