An unusual spectrally reproducible near‐IR random lasing (RL) with no fluctuation of lasing peak wavelength is disclosed in polycrystalline films of formamidinium tin triiodide perovskite, which have been chemically stabilized against Sn²⁺ to Sn⁴⁺ oxidation. Remarkably, a quality Q‐factor as high as ≈10⁴ with an amplified spontaneous emission (ASE) threshold as low as 2 µJ cm⁻² (both at 20 K) are achieved. The observed spectral reproducibility is unprecedented for semiconductor thin film RL systems and cannot be explained by the strong spatial localization of lasing modes. Instead, it is suggested that the spectral stability is a result of such an unique property of Sn‐based perovskites as a large inhomogeneous broadening of the emitting centers, which is a consequence of an intrinsic structural inhomogeneity of the material. Due to this, lasing can occur simultaneously in modes that are spatially strongly overlapped, as long as the spectral separation between the modes is larger than the homogeneous linewidth of the emitting centers. The discovered mechanism of RL spectral stability in semiconductor materials, possessing inhomogeneous broadening, opens up prospects for their practical use as cheap sources of narrow laser lines.