Abstract: Viable magnetic fusion devices necessitate combining good confinement with effective power flux handling. A major concern for ITER, and devices beyond, is the divertor heat load width, which sets peak boundary heat loads on the plasma-facing materials. Current estimates of the heat flux width are narrow for future reactors. Here, we demonstrate how pedestal turbulence can expand into, or entrain, the stable scrape-off-layer and so broaden the heat flux width beyond these neoclassical predictions. Employing combined theoretical, computational, and experimental approaches, we focus on quiescent high confinement discharges on the DIII-D tokamak, but the results are of broader significance. Our findings uncover common trends in the edge turbulence intensity flux, the pressure perturbation skewness, and the turbulence mixing length, which together determine the heat flux width. This research demonstrates the physics of scrape-off-layer broadening by turbulence and highlights the promise of a turbulent pedestal for successful core-edge integration in ITER and future fusion devices.