The success of direct laser-driven inertial confinement fusion (ICF) relies critically on the efficient coupling of laser light to plasma. At ignition scale, the absolute stimulated Raman scattering (SRS) instability can severely inhibit this coupling by redirecting and strongly depleting laser light. This Letter describes a new dynamic saturation regime of the absolute SRS instability. The saturation occurs when spatiotemporal fluctuations in the ion-acoustic density detune the instability resonance. The dynamic saturation mitigates the strong depletion of laser light and enhances its transmission through the instability region, explaining the coupling of laser light to ICF targets at higher plasma densities.