The utilization of crude glycerol, generated as a by-product from the biodiesel production process, for the production of high value-added products represents an opportunity to overcome the negative impact of low glycerol prices in the biodiesel industry. In this study, the biochemical behavior of Yarrowia lipolytica strains FMCC Y-74 and FMCC Y-75 was investigated using glycerol as a carbon source. Initially, the effect of pH value (3.0–7.0) was examined to produce polyols, intracellular lipids, and polysaccharides. At low pH values (initial pH 3.0–5.0), significant mannitol production was recorded. The highest mannitol production (19.64 g L−1) was obtained by Y. lipolytica FMCC Y-74 at pH = 3.0. At pH values ranging between 5.0 and 6.0, intracellular polysaccharides synthesis was favored, while polyols production was suppressed. Subsequently, the effect of crude glycerol and its concentration on polyols production was studied. Y. lipolytica FMCC Y-74 showed high tolerance to impurities of crude glycerol. Initial substrate concentrations influence polyols production and distribution with a metabolic shift toward erythritol production being observed when the initial glycerol concentration (Gly0) increased. The highest total polyols production (=56.64 g L−1) was obtained at Gly0 adjusted to ≈120 g L−1. The highest polyols conversion yield (0.59 g g−1) and productivity (4.36 g L−1 d−1) were reached at Gly0 = 80 g L−1. In fed-batch intermittent fermentation with glycerol concentration remaining ≤60 g L−1, the metabolism was shifted toward mannitol biosynthesis, which was the main polyol produced in significant quantities (=36.84 g L−1) with a corresponding conversion yield of 0.51 g g−1.