The development of efficient bioprocesses requires inexpensive and renewable substrates. Molasses, a by-product of the sugar industry, contains mostly sucrose, a disaccharide composed of glucose and fructose, both easily absorbed by microorganisms. Yarrowia lipolytica, a platform for the production of various chemicals, can be engineered for sucrose utilization by heterologous invertase expression, yet the problem of preferential use of glucose over fructose remains, as fructose consumption begins only after glucose depletion what significantly extends the bioprocesses. We investigated the role of hexose transporters and hexokinase (native and fructophilic) in this preference. Analysis of growth profiles and kinetics of monosaccharide utilization has proven that the glucose preference in Y. lipolytica depends primarily on the affinity of native hexokinase for glucose. Interestingly, combined overexpression of either hexokinase with hexose transporters significantly accelerated citric acid biosynthesis and enhanced pentose phosphate pathway leading to secretion of polyols (31.5 g/L vs. no polyols in the control strain). So far, polyol biosynthesis was efficient in glycerol-containing media. Moreover, overexpression of fructophilic hexokinase in combination with hexose transporters not only shortened this process to 48 h (84 h for the medium with glycerol) but also allowed to obtain 23% more polyols (40 g/L) compared to the glycerol medium (32.5 g/L).